Datasets:
id stringlengths 16 152 | package stringclasses 563
values | symbol stringlengths 1 125 | headline stringlengths 0 249 | usage stringlengths 0 722 | description stringclasses 11
values | example_code stringlengths 0 2.87k | example_output stringclasses 42
values | see_also stringlengths 0 1.59k | source_file stringclasses 602
values | branch stringclasses 1
value | text_for_embedding stringlengths 0 4.44k | raw_text stringlengths 14 77.1k |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
AnisotropicDimensionDoc_09c089b7_getAnisotropicDimensionQQp | AnisotropicDimensionDoc | getAnisotropicDimensionQQp | returns the anisotropic dimension of a rational symmetric bilinear form over the p-adic rational numbers | getAnisotropicDimensionQQp(beta, p) | getAnisotropicDimension | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/AnisotropicDimensionDoc.m2 | stable | HEADLINE: returns the anisotropic dimension of a rational symmetric bilinear form over the p-adic rational numbers
USAGE: getAnisotropicDimensionQQp(beta, p)
INPUTS: beta: GrothendieckWittClass
over $\mathbb{Q}$
p: ZZ
a prime number
OUTPUTS: : ZZ
the rank of the anisotropic part ... | Key
getAnisotropicDimensionQQp
(getAnisotropicDimensionQQp, GrothendieckWittClass, ZZ)
Headline
returns the anisotropic dimension of a rational symmetric bilinear form over the p-adic rational numbers
Usage
getAnisotropicDimensionQQp(beta, p)
Inputs
beta: GrothendieckWittCl... | |||
AnisotropicDimensionDoc_09c089b7_(getAnisotropicDimensionQQp,_GrothendieckWittClass,_ZZ) | AnisotropicDimensionDoc | (getAnisotropicDimensionQQp, GrothendieckWittClass, ZZ) | returns the anisotropic dimension of a rational symmetric bilinear form over the p-adic rational numbers | getAnisotropicDimensionQQp(beta, p) | getAnisotropicDimension | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/AnisotropicDimensionDoc.m2 | stable | HEADLINE: returns the anisotropic dimension of a rational symmetric bilinear form over the p-adic rational numbers
USAGE: getAnisotropicDimensionQQp(beta, p)
INPUTS: beta: GrothendieckWittClass
over $\mathbb{Q}$
p: ZZ
a prime number
OUTPUTS: : ZZ
the rank of the anisotropic part ... | Key
getAnisotropicDimensionQQp
(getAnisotropicDimensionQQp, GrothendieckWittClass, ZZ)
Headline
returns the anisotropic dimension of a rational symmetric bilinear form over the p-adic rational numbers
Usage
getAnisotropicDimensionQQp(beta, p)
Inputs
beta: GrothendieckWittCl... | |||
AnisotropicDimensionDoc_d98fe29b_getAnisotropicDimension | AnisotropicDimensionDoc | getAnisotropicDimension | returns the anisotropic dimension of a symmetric bilinear form | getAnisotropicDimension beta | getWittIndex
getAnisotropicDimensionQQp
getAnisotropicPart | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/AnisotropicDimensionDoc.m2 | stable | HEADLINE: returns the anisotropic dimension of a symmetric bilinear form
USAGE: getAnisotropicDimension beta
INPUTS: beta: GrothendieckWittClass
a GrothendieckWittClass over a field $k$, where $k$ is $\mathbb{Q}$, $\mathbb{R}$, $\mathbb{C}$, or a finite field of characteristic not 2
OUTPUTS: : ZZ
... | Key
getAnisotropicDimension
(getAnisotropicDimension, GrothendieckWittClass)
(getAnisotropicDimension, Matrix)
Headline
returns the anisotropic dimension of a symmetric bilinear form
Usage
getAnisotropicDimension beta
Inputs
beta: GrothendieckWittClass
... | |||
AnisotropicDimensionDoc_d98fe29b_(getAnisotropicDimension,_GrothendieckWittClass) | AnisotropicDimensionDoc | (getAnisotropicDimension, GrothendieckWittClass) | returns the anisotropic dimension of a symmetric bilinear form | getAnisotropicDimension beta | getWittIndex
getAnisotropicDimensionQQp
getAnisotropicPart | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/AnisotropicDimensionDoc.m2 | stable | HEADLINE: returns the anisotropic dimension of a symmetric bilinear form
USAGE: getAnisotropicDimension beta
INPUTS: beta: GrothendieckWittClass
a GrothendieckWittClass over a field $k$, where $k$ is $\mathbb{Q}$, $\mathbb{R}$, $\mathbb{C}$, or a finite field of characteristic not 2
OUTPUTS: : ZZ
... | Key
getAnisotropicDimension
(getAnisotropicDimension, GrothendieckWittClass)
(getAnisotropicDimension, Matrix)
Headline
returns the anisotropic dimension of a symmetric bilinear form
Usage
getAnisotropicDimension beta
Inputs
beta: GrothendieckWittClass
... | |||
AnisotropicDimensionDoc_d98fe29b_(getAnisotropicDimension,__Matrix) | AnisotropicDimensionDoc | (getAnisotropicDimension, Matrix) | returns the anisotropic dimension of a symmetric bilinear form | getAnisotropicDimension beta | getWittIndex
getAnisotropicDimensionQQp
getAnisotropicPart | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/AnisotropicDimensionDoc.m2 | stable | HEADLINE: returns the anisotropic dimension of a symmetric bilinear form
USAGE: getAnisotropicDimension beta
INPUTS: beta: GrothendieckWittClass
a GrothendieckWittClass over a field $k$, where $k$ is $\mathbb{Q}$, $\mathbb{R}$, $\mathbb{C}$, or a finite field of characteristic not 2
OUTPUTS: : ZZ
... | Key
getAnisotropicDimension
(getAnisotropicDimension, GrothendieckWittClass)
(getAnisotropicDimension, Matrix)
Headline
returns the anisotropic dimension of a symmetric bilinear form
Usage
getAnisotropicDimension beta
Inputs
beta: GrothendieckWittClass
... | |||
AnisotropicDimensionDoc_a7fd51a3_getWittIndex | AnisotropicDimensionDoc | getWittIndex | returns the Witt index of a symmetric bilinear form | getWittIndex beta | getAnisotropicDimension | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/AnisotropicDimensionDoc.m2 | stable | HEADLINE: returns the Witt index of a symmetric bilinear form
USAGE: getWittIndex beta
INPUTS: beta: GrothendieckWittClass
a GrothendieckWittClass denoted by $\beta\in\text{GW}(k)$, where $k$ is $\mathbb{Q}$, $\mathbb{R}$, $\mathbb{C}$, or a finite field of characteristic not 2
OUTPUTS: : ZZ
... | Key
getWittIndex
(getWittIndex, GrothendieckWittClass)
Headline
returns the Witt index of a symmetric bilinear form
Usage
getWittIndex beta
Inputs
beta: GrothendieckWittClass
a GrothendieckWittClass denoted by $\beta\in\text{GW}(k)$, where $k$ is $\math... | |||
AnisotropicDimensionDoc_a7fd51a3_(getWittIndex,_GrothendieckWittClass) | AnisotropicDimensionDoc | (getWittIndex, GrothendieckWittClass) | returns the Witt index of a symmetric bilinear form | getWittIndex beta | getAnisotropicDimension | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/AnisotropicDimensionDoc.m2 | stable | HEADLINE: returns the Witt index of a symmetric bilinear form
USAGE: getWittIndex beta
INPUTS: beta: GrothendieckWittClass
a GrothendieckWittClass denoted by $\beta\in\text{GW}(k)$, where $k$ is $\mathbb{Q}$, $\mathbb{R}$, $\mathbb{C}$, or a finite field of characteristic not 2
OUTPUTS: : ZZ
... | Key
getWittIndex
(getWittIndex, GrothendieckWittClass)
Headline
returns the Witt index of a symmetric bilinear form
Usage
getWittIndex beta
Inputs
beta: GrothendieckWittClass
a GrothendieckWittClass denoted by $\beta\in\text{GW}(k)$, where $k$ is $\math... | |||
ArithmeticMethodsDoc_251ca2aa_getPadicValuation | ArithmeticMethodsDoc | getPadicValuation | p-adic valuation of a rational number | getPadicValuation(a, p) | a = 363/7;
getPadicValuation(a, 11) | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/ArithmeticMethodsDoc.m2 | stable | HEADLINE: p-adic valuation of a rational number
USAGE: getPadicValuation(a, p)
INPUTS: a: QQ
a non-zero rational number in $\mathbb{Q}_p$
p: ZZ
a prime number
OUTPUTS: : ZZ
$n$ where $a=up^n$ and $u$ is a unit in $\mathbb{Z}_p$
EXAMPLE CODE:
```macaulay2
a = 363/7;
getPadicValuation(a, 11)
``` | Key
getPadicValuation
(getPadicValuation, ZZ, ZZ)
(getPadicValuation, QQ, ZZ)
Headline
p-adic valuation of a rational number
Usage
getPadicValuation(a, p)
Inputs
a: QQ
a non-zero rational number in $\mathbb{Q}_p$
p: ZZ
a prime number
Outputs
: ZZ
$n$ where $a=up^n$ and $u$ is a unit in $\ma... | |||
ArithmeticMethodsDoc_251ca2aa_(getPadicValuation,_ZZ,_ZZ) | ArithmeticMethodsDoc | (getPadicValuation, ZZ, ZZ) | p-adic valuation of a rational number | getPadicValuation(a, p) | a = 363/7;
getPadicValuation(a, 11) | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/ArithmeticMethodsDoc.m2 | stable | HEADLINE: p-adic valuation of a rational number
USAGE: getPadicValuation(a, p)
INPUTS: a: QQ
a non-zero rational number in $\mathbb{Q}_p$
p: ZZ
a prime number
OUTPUTS: : ZZ
$n$ where $a=up^n$ and $u$ is a unit in $\mathbb{Z}_p$
EXAMPLE CODE:
```macaulay2
a = 363/7;
getPadicValuation(a, 11)
``` | Key
getPadicValuation
(getPadicValuation, ZZ, ZZ)
(getPadicValuation, QQ, ZZ)
Headline
p-adic valuation of a rational number
Usage
getPadicValuation(a, p)
Inputs
a: QQ
a non-zero rational number in $\mathbb{Q}_p$
p: ZZ
a prime number
Outputs
: ZZ
$n$ where $a=up^n$ and $u$ is a unit in $\ma... | |||
ArithmeticMethodsDoc_251ca2aa_(getPadicValuation,_QQ,_ZZ) | ArithmeticMethodsDoc | (getPadicValuation, QQ, ZZ) | p-adic valuation of a rational number | getPadicValuation(a, p) | a = 363/7;
getPadicValuation(a, 11) | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/ArithmeticMethodsDoc.m2 | stable | HEADLINE: p-adic valuation of a rational number
USAGE: getPadicValuation(a, p)
INPUTS: a: QQ
a non-zero rational number in $\mathbb{Q}_p$
p: ZZ
a prime number
OUTPUTS: : ZZ
$n$ where $a=up^n$ and $u$ is a unit in $\mathbb{Z}_p$
EXAMPLE CODE:
```macaulay2
a = 363/7;
getPadicValuation(a, 11)
``` | Key
getPadicValuation
(getPadicValuation, ZZ, ZZ)
(getPadicValuation, QQ, ZZ)
Headline
p-adic valuation of a rational number
Usage
getPadicValuation(a, p)
Inputs
a: QQ
a non-zero rational number in $\mathbb{Q}_p$
p: ZZ
a prime number
Outputs
: ZZ
$n$ where $a=up^n$ and $u$ is a unit in $\ma... | |||
ArithmeticMethodsDoc_13f18f4e_getLocalAlgebraBasis | ArithmeticMethodsDoc | getLocalAlgebraBasis | produces a basis for a local finitely generated algebra over a field or finite étale algebra | getLocalAlgebraBasis(L, p) | QQ[x,y];
f = {x^2 + 1 - y, y};
p = ideal(x^2 + 1, y);
getLocalAlgebraBasis(f, p) | getLocalA1Degree | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/ArithmeticMethodsDoc.m2 | stable | HEADLINE: produces a basis for a local finitely generated algebra over a field or finite étale algebra
USAGE: getLocalAlgebraBasis(L, p)
INPUTS: L: List
of polynomials $f=(f_1, \dots ,f_n)$ over the same ring
p: Ideal
a prime ideal of an isolated zero
OUTPUTS: : List
of basis elements of the local algebra... | Key
getLocalAlgebraBasis
(getLocalAlgebraBasis, List, Ideal)
Headline
produces a basis for a local finitely generated algebra over a field or finite étale algebra
Usage
getLocalAlgebraBasis(L, p)
Inputs
L: List
of polynomials $f=(f_1, \dots ,f_n)$ over the same ring
p: Ideal
a prime ideal of an iso... | ||
ArithmeticMethodsDoc_13f18f4e_(getLocalAlgebraBasis,_List,_Ideal) | ArithmeticMethodsDoc | (getLocalAlgebraBasis, List, Ideal) | produces a basis for a local finitely generated algebra over a field or finite étale algebra | getLocalAlgebraBasis(L, p) | QQ[x,y];
f = {x^2 + 1 - y, y};
p = ideal(x^2 + 1, y);
getLocalAlgebraBasis(f, p) | getLocalA1Degree | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/ArithmeticMethodsDoc.m2 | stable | HEADLINE: produces a basis for a local finitely generated algebra over a field or finite étale algebra
USAGE: getLocalAlgebraBasis(L, p)
INPUTS: L: List
of polynomials $f=(f_1, \dots ,f_n)$ over the same ring
p: Ideal
a prime ideal of an isolated zero
OUTPUTS: : List
of basis elements of the local algebra... | Key
getLocalAlgebraBasis
(getLocalAlgebraBasis, List, Ideal)
Headline
produces a basis for a local finitely generated algebra over a field or finite étale algebra
Usage
getLocalAlgebraBasis(L, p)
Inputs
L: List
of polynomials $f=(f_1, \dots ,f_n)$ over the same ring
p: Ideal
a prime ideal of an iso... | ||
BuildingFormsDoc_b1894225_makeDiagonalForm | BuildingFormsDoc | makeDiagonalForm | the Grothendieck-Witt class of a diagonal form | makeDiagonalForm(k, a)
makeDiagonalForm(k, L) | makeDiagonalForm(GF(29), 5/13)
makeDiagonalForm(RR, 2) | getDiagonalClass
diagonalizeViaCongruence
getDiagonalEntries | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the Grothendieck-Witt class of a diagonal form
USAGE: makeDiagonalForm(k, a)
makeDiagonalForm(k, L)
INPUTS: k: Ring
a field or finite étale algebra over a field
a: RingElement
any element in the field or finite étale algebra over a field
L: Sequence
of elements in the field or finite étale al... | Key
makeDiagonalForm
(makeDiagonalForm, Ring, RingElement)
(makeDiagonalForm, Ring, Number)
(makeDiagonalForm, Ring, Sequence)
(makeDiagonalForm, InexactFieldFamily, RingElement)
(makeDiagonalForm, InexactFieldFamily, Number)
(makeDiagonalForm, InexactFieldFamily, Sequence)
Headline
the Grothendieck-Wi... | ||
BuildingFormsDoc_b1894225_(makeDiagonalForm,_Ring,_RingElement) | BuildingFormsDoc | (makeDiagonalForm, Ring, RingElement) | the Grothendieck-Witt class of a diagonal form | makeDiagonalForm(k, a)
makeDiagonalForm(k, L) | makeDiagonalForm(GF(29), 5/13)
makeDiagonalForm(RR, 2) | getDiagonalClass
diagonalizeViaCongruence
getDiagonalEntries | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the Grothendieck-Witt class of a diagonal form
USAGE: makeDiagonalForm(k, a)
makeDiagonalForm(k, L)
INPUTS: k: Ring
a field or finite étale algebra over a field
a: RingElement
any element in the field or finite étale algebra over a field
L: Sequence
of elements in the field or finite étale al... | Key
makeDiagonalForm
(makeDiagonalForm, Ring, RingElement)
(makeDiagonalForm, Ring, Number)
(makeDiagonalForm, Ring, Sequence)
(makeDiagonalForm, InexactFieldFamily, RingElement)
(makeDiagonalForm, InexactFieldFamily, Number)
(makeDiagonalForm, InexactFieldFamily, Sequence)
Headline
the Grothendieck-Wi... | ||
BuildingFormsDoc_b1894225_(makeDiagonalForm,_Ring,_Number) | BuildingFormsDoc | (makeDiagonalForm, Ring, Number) | the Grothendieck-Witt class of a diagonal form | makeDiagonalForm(k, a)
makeDiagonalForm(k, L) | makeDiagonalForm(GF(29), 5/13)
makeDiagonalForm(RR, 2) | getDiagonalClass
diagonalizeViaCongruence
getDiagonalEntries | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the Grothendieck-Witt class of a diagonal form
USAGE: makeDiagonalForm(k, a)
makeDiagonalForm(k, L)
INPUTS: k: Ring
a field or finite étale algebra over a field
a: RingElement
any element in the field or finite étale algebra over a field
L: Sequence
of elements in the field or finite étale al... | Key
makeDiagonalForm
(makeDiagonalForm, Ring, RingElement)
(makeDiagonalForm, Ring, Number)
(makeDiagonalForm, Ring, Sequence)
(makeDiagonalForm, InexactFieldFamily, RingElement)
(makeDiagonalForm, InexactFieldFamily, Number)
(makeDiagonalForm, InexactFieldFamily, Sequence)
Headline
the Grothendieck-Wi... | ||
BuildingFormsDoc_b1894225_(makeDiagonalForm,_Ring,_Sequence) | BuildingFormsDoc | (makeDiagonalForm, Ring, Sequence) | the Grothendieck-Witt class of a diagonal form | makeDiagonalForm(k, a)
makeDiagonalForm(k, L) | makeDiagonalForm(GF(29), 5/13)
makeDiagonalForm(RR, 2) | getDiagonalClass
diagonalizeViaCongruence
getDiagonalEntries | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the Grothendieck-Witt class of a diagonal form
USAGE: makeDiagonalForm(k, a)
makeDiagonalForm(k, L)
INPUTS: k: Ring
a field or finite étale algebra over a field
a: RingElement
any element in the field or finite étale algebra over a field
L: Sequence
of elements in the field or finite étale al... | Key
makeDiagonalForm
(makeDiagonalForm, Ring, RingElement)
(makeDiagonalForm, Ring, Number)
(makeDiagonalForm, Ring, Sequence)
(makeDiagonalForm, InexactFieldFamily, RingElement)
(makeDiagonalForm, InexactFieldFamily, Number)
(makeDiagonalForm, InexactFieldFamily, Sequence)
Headline
the Grothendieck-Wi... | ||
BuildingFormsDoc_b1894225_(makeDiagonalForm,_InexactFieldFamily,_RingElement) | BuildingFormsDoc | (makeDiagonalForm, InexactFieldFamily, RingElement) | the Grothendieck-Witt class of a diagonal form | makeDiagonalForm(k, a)
makeDiagonalForm(k, L) | makeDiagonalForm(GF(29), 5/13)
makeDiagonalForm(RR, 2) | getDiagonalClass
diagonalizeViaCongruence
getDiagonalEntries | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the Grothendieck-Witt class of a diagonal form
USAGE: makeDiagonalForm(k, a)
makeDiagonalForm(k, L)
INPUTS: k: Ring
a field or finite étale algebra over a field
a: RingElement
any element in the field or finite étale algebra over a field
L: Sequence
of elements in the field or finite étale al... | Key
makeDiagonalForm
(makeDiagonalForm, Ring, RingElement)
(makeDiagonalForm, Ring, Number)
(makeDiagonalForm, Ring, Sequence)
(makeDiagonalForm, InexactFieldFamily, RingElement)
(makeDiagonalForm, InexactFieldFamily, Number)
(makeDiagonalForm, InexactFieldFamily, Sequence)
Headline
the Grothendieck-Wi... | ||
BuildingFormsDoc_b1894225_(makeDiagonalForm,_InexactFieldFamily,_Number) | BuildingFormsDoc | (makeDiagonalForm, InexactFieldFamily, Number) | the Grothendieck-Witt class of a diagonal form | makeDiagonalForm(k, a)
makeDiagonalForm(k, L) | makeDiagonalForm(GF(29), 5/13)
makeDiagonalForm(RR, 2) | getDiagonalClass
diagonalizeViaCongruence
getDiagonalEntries | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the Grothendieck-Witt class of a diagonal form
USAGE: makeDiagonalForm(k, a)
makeDiagonalForm(k, L)
INPUTS: k: Ring
a field or finite étale algebra over a field
a: RingElement
any element in the field or finite étale algebra over a field
L: Sequence
of elements in the field or finite étale al... | Key
makeDiagonalForm
(makeDiagonalForm, Ring, RingElement)
(makeDiagonalForm, Ring, Number)
(makeDiagonalForm, Ring, Sequence)
(makeDiagonalForm, InexactFieldFamily, RingElement)
(makeDiagonalForm, InexactFieldFamily, Number)
(makeDiagonalForm, InexactFieldFamily, Sequence)
Headline
the Grothendieck-Wi... | ||
BuildingFormsDoc_b1894225_(makeDiagonalForm,_InexactFieldFamily,_Sequence) | BuildingFormsDoc | (makeDiagonalForm, InexactFieldFamily, Sequence) | the Grothendieck-Witt class of a diagonal form | makeDiagonalForm(k, a)
makeDiagonalForm(k, L) | makeDiagonalForm(GF(29), 5/13)
makeDiagonalForm(RR, 2) | getDiagonalClass
diagonalizeViaCongruence
getDiagonalEntries | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the Grothendieck-Witt class of a diagonal form
USAGE: makeDiagonalForm(k, a)
makeDiagonalForm(k, L)
INPUTS: k: Ring
a field or finite étale algebra over a field
a: RingElement
any element in the field or finite étale algebra over a field
L: Sequence
of elements in the field or finite étale al... | Key
makeDiagonalForm
(makeDiagonalForm, Ring, RingElement)
(makeDiagonalForm, Ring, Number)
(makeDiagonalForm, Ring, Sequence)
(makeDiagonalForm, InexactFieldFamily, RingElement)
(makeDiagonalForm, InexactFieldFamily, Number)
(makeDiagonalForm, InexactFieldFamily, Sequence)
Headline
the Grothendieck-Wi... | ||
BuildingFormsDoc_e9e14b0b_makePfisterForm | BuildingFormsDoc | makePfisterForm | the Grothendieck-Witt class of a Pfister form | makePfisterForm(k, a)
makePfisterForm(k, L) | makePfisterForm(GF(13), -2/3)
makePfisterForm(CC, 3) | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the Grothendieck-Witt class of a Pfister form
USAGE: makePfisterForm(k, a)
makePfisterForm(k, L)
INPUTS: k: Ring
a field of characteristic not 2
a: RingElement
any element in the field
L: Sequence
of elements in the field $a_{i}$ where $i = 1,\dots, n$
OUTPUTS: : GrothendieckWittClass
the... | Key
makePfisterForm
(makePfisterForm, Ring, RingElement)
(makePfisterForm, Ring, Number)
(makePfisterForm, Ring, Sequence)
(makePfisterForm, InexactFieldFamily, RingElement)
(makePfisterForm, InexactFieldFamily, Number)
(makePfisterForm, InexactFieldFamily, Sequence)
Headline
the Grothendieck-Witt clas... | |||
BuildingFormsDoc_e9e14b0b_(makePfisterForm,_Ring,_RingElement) | BuildingFormsDoc | (makePfisterForm, Ring, RingElement) | the Grothendieck-Witt class of a Pfister form | makePfisterForm(k, a)
makePfisterForm(k, L) | makePfisterForm(GF(13), -2/3)
makePfisterForm(CC, 3) | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the Grothendieck-Witt class of a Pfister form
USAGE: makePfisterForm(k, a)
makePfisterForm(k, L)
INPUTS: k: Ring
a field of characteristic not 2
a: RingElement
any element in the field
L: Sequence
of elements in the field $a_{i}$ where $i = 1,\dots, n$
OUTPUTS: : GrothendieckWittClass
the... | Key
makePfisterForm
(makePfisterForm, Ring, RingElement)
(makePfisterForm, Ring, Number)
(makePfisterForm, Ring, Sequence)
(makePfisterForm, InexactFieldFamily, RingElement)
(makePfisterForm, InexactFieldFamily, Number)
(makePfisterForm, InexactFieldFamily, Sequence)
Headline
the Grothendieck-Witt clas... | |||
BuildingFormsDoc_e9e14b0b_(makePfisterForm,_Ring,_Number) | BuildingFormsDoc | (makePfisterForm, Ring, Number) | the Grothendieck-Witt class of a Pfister form | makePfisterForm(k, a)
makePfisterForm(k, L) | makePfisterForm(GF(13), -2/3)
makePfisterForm(CC, 3) | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the Grothendieck-Witt class of a Pfister form
USAGE: makePfisterForm(k, a)
makePfisterForm(k, L)
INPUTS: k: Ring
a field of characteristic not 2
a: RingElement
any element in the field
L: Sequence
of elements in the field $a_{i}$ where $i = 1,\dots, n$
OUTPUTS: : GrothendieckWittClass
the... | Key
makePfisterForm
(makePfisterForm, Ring, RingElement)
(makePfisterForm, Ring, Number)
(makePfisterForm, Ring, Sequence)
(makePfisterForm, InexactFieldFamily, RingElement)
(makePfisterForm, InexactFieldFamily, Number)
(makePfisterForm, InexactFieldFamily, Sequence)
Headline
the Grothendieck-Witt clas... | |||
BuildingFormsDoc_e9e14b0b_(makePfisterForm,_Ring,_Sequence) | BuildingFormsDoc | (makePfisterForm, Ring, Sequence) | the Grothendieck-Witt class of a Pfister form | makePfisterForm(k, a)
makePfisterForm(k, L) | makePfisterForm(GF(13), -2/3)
makePfisterForm(CC, 3) | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the Grothendieck-Witt class of a Pfister form
USAGE: makePfisterForm(k, a)
makePfisterForm(k, L)
INPUTS: k: Ring
a field of characteristic not 2
a: RingElement
any element in the field
L: Sequence
of elements in the field $a_{i}$ where $i = 1,\dots, n$
OUTPUTS: : GrothendieckWittClass
the... | Key
makePfisterForm
(makePfisterForm, Ring, RingElement)
(makePfisterForm, Ring, Number)
(makePfisterForm, Ring, Sequence)
(makePfisterForm, InexactFieldFamily, RingElement)
(makePfisterForm, InexactFieldFamily, Number)
(makePfisterForm, InexactFieldFamily, Sequence)
Headline
the Grothendieck-Witt clas... | |||
BuildingFormsDoc_e9e14b0b_(makePfisterForm,_InexactFieldFamily,_RingElement) | BuildingFormsDoc | (makePfisterForm, InexactFieldFamily, RingElement) | the Grothendieck-Witt class of a Pfister form | makePfisterForm(k, a)
makePfisterForm(k, L) | makePfisterForm(GF(13), -2/3)
makePfisterForm(CC, 3) | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the Grothendieck-Witt class of a Pfister form
USAGE: makePfisterForm(k, a)
makePfisterForm(k, L)
INPUTS: k: Ring
a field of characteristic not 2
a: RingElement
any element in the field
L: Sequence
of elements in the field $a_{i}$ where $i = 1,\dots, n$
OUTPUTS: : GrothendieckWittClass
the... | Key
makePfisterForm
(makePfisterForm, Ring, RingElement)
(makePfisterForm, Ring, Number)
(makePfisterForm, Ring, Sequence)
(makePfisterForm, InexactFieldFamily, RingElement)
(makePfisterForm, InexactFieldFamily, Number)
(makePfisterForm, InexactFieldFamily, Sequence)
Headline
the Grothendieck-Witt clas... | |||
BuildingFormsDoc_e9e14b0b_(makePfisterForm,_InexactFieldFamily,_Number) | BuildingFormsDoc | (makePfisterForm, InexactFieldFamily, Number) | the Grothendieck-Witt class of a Pfister form | makePfisterForm(k, a)
makePfisterForm(k, L) | makePfisterForm(GF(13), -2/3)
makePfisterForm(CC, 3) | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the Grothendieck-Witt class of a Pfister form
USAGE: makePfisterForm(k, a)
makePfisterForm(k, L)
INPUTS: k: Ring
a field of characteristic not 2
a: RingElement
any element in the field
L: Sequence
of elements in the field $a_{i}$ where $i = 1,\dots, n$
OUTPUTS: : GrothendieckWittClass
the... | Key
makePfisterForm
(makePfisterForm, Ring, RingElement)
(makePfisterForm, Ring, Number)
(makePfisterForm, Ring, Sequence)
(makePfisterForm, InexactFieldFamily, RingElement)
(makePfisterForm, InexactFieldFamily, Number)
(makePfisterForm, InexactFieldFamily, Sequence)
Headline
the Grothendieck-Witt clas... | |||
BuildingFormsDoc_e9e14b0b_(makePfisterForm,_InexactFieldFamily,_Sequence) | BuildingFormsDoc | (makePfisterForm, InexactFieldFamily, Sequence) | the Grothendieck-Witt class of a Pfister form | makePfisterForm(k, a)
makePfisterForm(k, L) | makePfisterForm(GF(13), -2/3)
makePfisterForm(CC, 3) | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the Grothendieck-Witt class of a Pfister form
USAGE: makePfisterForm(k, a)
makePfisterForm(k, L)
INPUTS: k: Ring
a field of characteristic not 2
a: RingElement
any element in the field
L: Sequence
of elements in the field $a_{i}$ where $i = 1,\dots, n$
OUTPUTS: : GrothendieckWittClass
the... | Key
makePfisterForm
(makePfisterForm, Ring, RingElement)
(makePfisterForm, Ring, Number)
(makePfisterForm, Ring, Sequence)
(makePfisterForm, InexactFieldFamily, RingElement)
(makePfisterForm, InexactFieldFamily, Number)
(makePfisterForm, InexactFieldFamily, Sequence)
Headline
the Grothendieck-Witt clas... | |||
BuildingFormsDoc_9849c769_makeHyperbolicForm | BuildingFormsDoc | makeHyperbolicForm | the Grothendieck-Witt class of a hyperbolic form | makeHyperbolicForm(k)
makeHyperbolicForm(k, n) | makeHyperbolicForm(RR, 4) | isAnisotropic
getSumDecomposition
getSumDecompositionString | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the Grothendieck-Witt class of a hyperbolic form
USAGE: makeHyperbolicForm(k)
makeHyperbolicForm(k, n)
INPUTS: k: Ring
a field or finite étale algebra over a field
n: ZZ
an even number, giving an optional rank $n$ for a totally hyperbolic form
OUTPUTS: : GrothendieckWittClass
the hyperbolic fo... | Key
makeHyperbolicForm
(makeHyperbolicForm, Ring)
(makeHyperbolicForm, Ring, ZZ)
(makeHyperbolicForm, InexactFieldFamily)
(makeHyperbolicForm, InexactFieldFamily, ZZ)
Headline
the Grothendieck-Witt class of a hyperbolic form
Usage
makeHyperbolicForm(k)
makeHyperbolicForm(k, n)
Inputs
k: Ring
a f... | ||
BuildingFormsDoc_9849c769_(makeHyperbolicForm,_Ring) | BuildingFormsDoc | (makeHyperbolicForm, Ring) | the Grothendieck-Witt class of a hyperbolic form | makeHyperbolicForm(k)
makeHyperbolicForm(k, n) | makeHyperbolicForm(RR, 4) | isAnisotropic
getSumDecomposition
getSumDecompositionString | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the Grothendieck-Witt class of a hyperbolic form
USAGE: makeHyperbolicForm(k)
makeHyperbolicForm(k, n)
INPUTS: k: Ring
a field or finite étale algebra over a field
n: ZZ
an even number, giving an optional rank $n$ for a totally hyperbolic form
OUTPUTS: : GrothendieckWittClass
the hyperbolic fo... | Key
makeHyperbolicForm
(makeHyperbolicForm, Ring)
(makeHyperbolicForm, Ring, ZZ)
(makeHyperbolicForm, InexactFieldFamily)
(makeHyperbolicForm, InexactFieldFamily, ZZ)
Headline
the Grothendieck-Witt class of a hyperbolic form
Usage
makeHyperbolicForm(k)
makeHyperbolicForm(k, n)
Inputs
k: Ring
a f... | ||
BuildingFormsDoc_9849c769_(makeHyperbolicForm,_Ring,_ZZ) | BuildingFormsDoc | (makeHyperbolicForm, Ring, ZZ) | the Grothendieck-Witt class of a hyperbolic form | makeHyperbolicForm(k)
makeHyperbolicForm(k, n) | makeHyperbolicForm(RR, 4) | isAnisotropic
getSumDecomposition
getSumDecompositionString | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the Grothendieck-Witt class of a hyperbolic form
USAGE: makeHyperbolicForm(k)
makeHyperbolicForm(k, n)
INPUTS: k: Ring
a field or finite étale algebra over a field
n: ZZ
an even number, giving an optional rank $n$ for a totally hyperbolic form
OUTPUTS: : GrothendieckWittClass
the hyperbolic fo... | Key
makeHyperbolicForm
(makeHyperbolicForm, Ring)
(makeHyperbolicForm, Ring, ZZ)
(makeHyperbolicForm, InexactFieldFamily)
(makeHyperbolicForm, InexactFieldFamily, ZZ)
Headline
the Grothendieck-Witt class of a hyperbolic form
Usage
makeHyperbolicForm(k)
makeHyperbolicForm(k, n)
Inputs
k: Ring
a f... | ||
BuildingFormsDoc_9849c769_(makeHyperbolicForm,_InexactFieldFamily) | BuildingFormsDoc | (makeHyperbolicForm, InexactFieldFamily) | the Grothendieck-Witt class of a hyperbolic form | makeHyperbolicForm(k)
makeHyperbolicForm(k, n) | makeHyperbolicForm(RR, 4) | isAnisotropic
getSumDecomposition
getSumDecompositionString | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the Grothendieck-Witt class of a hyperbolic form
USAGE: makeHyperbolicForm(k)
makeHyperbolicForm(k, n)
INPUTS: k: Ring
a field or finite étale algebra over a field
n: ZZ
an even number, giving an optional rank $n$ for a totally hyperbolic form
OUTPUTS: : GrothendieckWittClass
the hyperbolic fo... | Key
makeHyperbolicForm
(makeHyperbolicForm, Ring)
(makeHyperbolicForm, Ring, ZZ)
(makeHyperbolicForm, InexactFieldFamily)
(makeHyperbolicForm, InexactFieldFamily, ZZ)
Headline
the Grothendieck-Witt class of a hyperbolic form
Usage
makeHyperbolicForm(k)
makeHyperbolicForm(k, n)
Inputs
k: Ring
a f... | ||
BuildingFormsDoc_9849c769_(makeHyperbolicForm,_InexactFieldFamily,_ZZ) | BuildingFormsDoc | (makeHyperbolicForm, InexactFieldFamily, ZZ) | the Grothendieck-Witt class of a hyperbolic form | makeHyperbolicForm(k)
makeHyperbolicForm(k, n) | makeHyperbolicForm(RR, 4) | isAnisotropic
getSumDecomposition
getSumDecompositionString | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the Grothendieck-Witt class of a hyperbolic form
USAGE: makeHyperbolicForm(k)
makeHyperbolicForm(k, n)
INPUTS: k: Ring
a field or finite étale algebra over a field
n: ZZ
an even number, giving an optional rank $n$ for a totally hyperbolic form
OUTPUTS: : GrothendieckWittClass
the hyperbolic fo... | Key
makeHyperbolicForm
(makeHyperbolicForm, Ring)
(makeHyperbolicForm, Ring, ZZ)
(makeHyperbolicForm, InexactFieldFamily)
(makeHyperbolicForm, InexactFieldFamily, ZZ)
Headline
the Grothendieck-Witt class of a hyperbolic form
Usage
makeHyperbolicForm(k)
makeHyperbolicForm(k, n)
Inputs
k: Ring
a f... | ||
BuildingFormsDoc_01517dde_makeDiagonalUnstableForm | BuildingFormsDoc | makeDiagonalUnstableForm | the unstable Grothendieck-Witt class of a diagonal matrix | makeDiagonalUnstableForm(k, a)
makeDiagonalUnstableForm(k, L) | makeDiagonalUnstableForm(GF(29), 5/13)
makeDiagonalUnstableForm(RR, 2) | getDiagonalClass
diagonalizeViaCongruence | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the unstable Grothendieck-Witt class of a diagonal matrix
USAGE: makeDiagonalUnstableForm(k, a)
makeDiagonalUnstableForm(k, L)
INPUTS: k: Ring
a field or finite étale algebra over a field
a: RingElement
any element in the field or finite étale algebra over a field
L: Sequence
of elements in t... | Key
makeDiagonalUnstableForm
(makeDiagonalUnstableForm, Ring, RingElement)
(makeDiagonalUnstableForm, Ring, Number)
(makeDiagonalUnstableForm, Ring, Sequence)
(makeDiagonalUnstableForm, InexactFieldFamily, RingElement)
(makeDiagonalUnstableForm, InexactFieldFamily, Number)
(makeDiagonalUnstableForm, Inexa... | ||
BuildingFormsDoc_01517dde_(makeDiagonalUnstableForm,_Ring,_RingElement) | BuildingFormsDoc | (makeDiagonalUnstableForm, Ring, RingElement) | the unstable Grothendieck-Witt class of a diagonal matrix | makeDiagonalUnstableForm(k, a)
makeDiagonalUnstableForm(k, L) | makeDiagonalUnstableForm(GF(29), 5/13)
makeDiagonalUnstableForm(RR, 2) | getDiagonalClass
diagonalizeViaCongruence | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the unstable Grothendieck-Witt class of a diagonal matrix
USAGE: makeDiagonalUnstableForm(k, a)
makeDiagonalUnstableForm(k, L)
INPUTS: k: Ring
a field or finite étale algebra over a field
a: RingElement
any element in the field or finite étale algebra over a field
L: Sequence
of elements in t... | Key
makeDiagonalUnstableForm
(makeDiagonalUnstableForm, Ring, RingElement)
(makeDiagonalUnstableForm, Ring, Number)
(makeDiagonalUnstableForm, Ring, Sequence)
(makeDiagonalUnstableForm, InexactFieldFamily, RingElement)
(makeDiagonalUnstableForm, InexactFieldFamily, Number)
(makeDiagonalUnstableForm, Inexa... | ||
BuildingFormsDoc_01517dde_(makeDiagonalUnstableForm,_Ring,_Number) | BuildingFormsDoc | (makeDiagonalUnstableForm, Ring, Number) | the unstable Grothendieck-Witt class of a diagonal matrix | makeDiagonalUnstableForm(k, a)
makeDiagonalUnstableForm(k, L) | makeDiagonalUnstableForm(GF(29), 5/13)
makeDiagonalUnstableForm(RR, 2) | getDiagonalClass
diagonalizeViaCongruence | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the unstable Grothendieck-Witt class of a diagonal matrix
USAGE: makeDiagonalUnstableForm(k, a)
makeDiagonalUnstableForm(k, L)
INPUTS: k: Ring
a field or finite étale algebra over a field
a: RingElement
any element in the field or finite étale algebra over a field
L: Sequence
of elements in t... | Key
makeDiagonalUnstableForm
(makeDiagonalUnstableForm, Ring, RingElement)
(makeDiagonalUnstableForm, Ring, Number)
(makeDiagonalUnstableForm, Ring, Sequence)
(makeDiagonalUnstableForm, InexactFieldFamily, RingElement)
(makeDiagonalUnstableForm, InexactFieldFamily, Number)
(makeDiagonalUnstableForm, Inexa... | ||
BuildingFormsDoc_01517dde_(makeDiagonalUnstableForm,_Ring,_Sequence) | BuildingFormsDoc | (makeDiagonalUnstableForm, Ring, Sequence) | the unstable Grothendieck-Witt class of a diagonal matrix | makeDiagonalUnstableForm(k, a)
makeDiagonalUnstableForm(k, L) | makeDiagonalUnstableForm(GF(29), 5/13)
makeDiagonalUnstableForm(RR, 2) | getDiagonalClass
diagonalizeViaCongruence | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the unstable Grothendieck-Witt class of a diagonal matrix
USAGE: makeDiagonalUnstableForm(k, a)
makeDiagonalUnstableForm(k, L)
INPUTS: k: Ring
a field or finite étale algebra over a field
a: RingElement
any element in the field or finite étale algebra over a field
L: Sequence
of elements in t... | Key
makeDiagonalUnstableForm
(makeDiagonalUnstableForm, Ring, RingElement)
(makeDiagonalUnstableForm, Ring, Number)
(makeDiagonalUnstableForm, Ring, Sequence)
(makeDiagonalUnstableForm, InexactFieldFamily, RingElement)
(makeDiagonalUnstableForm, InexactFieldFamily, Number)
(makeDiagonalUnstableForm, Inexa... | ||
BuildingFormsDoc_01517dde_(makeDiagonalUnstableForm,_InexactFieldFamily,_RingElement) | BuildingFormsDoc | (makeDiagonalUnstableForm, InexactFieldFamily, RingElement) | the unstable Grothendieck-Witt class of a diagonal matrix | makeDiagonalUnstableForm(k, a)
makeDiagonalUnstableForm(k, L) | makeDiagonalUnstableForm(GF(29), 5/13)
makeDiagonalUnstableForm(RR, 2) | getDiagonalClass
diagonalizeViaCongruence | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the unstable Grothendieck-Witt class of a diagonal matrix
USAGE: makeDiagonalUnstableForm(k, a)
makeDiagonalUnstableForm(k, L)
INPUTS: k: Ring
a field or finite étale algebra over a field
a: RingElement
any element in the field or finite étale algebra over a field
L: Sequence
of elements in t... | Key
makeDiagonalUnstableForm
(makeDiagonalUnstableForm, Ring, RingElement)
(makeDiagonalUnstableForm, Ring, Number)
(makeDiagonalUnstableForm, Ring, Sequence)
(makeDiagonalUnstableForm, InexactFieldFamily, RingElement)
(makeDiagonalUnstableForm, InexactFieldFamily, Number)
(makeDiagonalUnstableForm, Inexa... | ||
BuildingFormsDoc_01517dde_(makeDiagonalUnstableForm,_InexactFieldFamily,_Number) | BuildingFormsDoc | (makeDiagonalUnstableForm, InexactFieldFamily, Number) | the unstable Grothendieck-Witt class of a diagonal matrix | makeDiagonalUnstableForm(k, a)
makeDiagonalUnstableForm(k, L) | makeDiagonalUnstableForm(GF(29), 5/13)
makeDiagonalUnstableForm(RR, 2) | getDiagonalClass
diagonalizeViaCongruence | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the unstable Grothendieck-Witt class of a diagonal matrix
USAGE: makeDiagonalUnstableForm(k, a)
makeDiagonalUnstableForm(k, L)
INPUTS: k: Ring
a field or finite étale algebra over a field
a: RingElement
any element in the field or finite étale algebra over a field
L: Sequence
of elements in t... | Key
makeDiagonalUnstableForm
(makeDiagonalUnstableForm, Ring, RingElement)
(makeDiagonalUnstableForm, Ring, Number)
(makeDiagonalUnstableForm, Ring, Sequence)
(makeDiagonalUnstableForm, InexactFieldFamily, RingElement)
(makeDiagonalUnstableForm, InexactFieldFamily, Number)
(makeDiagonalUnstableForm, Inexa... | ||
BuildingFormsDoc_01517dde_(makeDiagonalUnstableForm,_InexactFieldFamily,_Sequence) | BuildingFormsDoc | (makeDiagonalUnstableForm, InexactFieldFamily, Sequence) | the unstable Grothendieck-Witt class of a diagonal matrix | makeDiagonalUnstableForm(k, a)
makeDiagonalUnstableForm(k, L) | makeDiagonalUnstableForm(GF(29), 5/13)
makeDiagonalUnstableForm(RR, 2) | getDiagonalClass
diagonalizeViaCongruence | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the unstable Grothendieck-Witt class of a diagonal matrix
USAGE: makeDiagonalUnstableForm(k, a)
makeDiagonalUnstableForm(k, L)
INPUTS: k: Ring
a field or finite étale algebra over a field
a: RingElement
any element in the field or finite étale algebra over a field
L: Sequence
of elements in t... | Key
makeDiagonalUnstableForm
(makeDiagonalUnstableForm, Ring, RingElement)
(makeDiagonalUnstableForm, Ring, Number)
(makeDiagonalUnstableForm, Ring, Sequence)
(makeDiagonalUnstableForm, InexactFieldFamily, RingElement)
(makeDiagonalUnstableForm, InexactFieldFamily, Number)
(makeDiagonalUnstableForm, Inexa... | ||
BuildingFormsDoc_a8fd4493_makeHyperbolicUnstableForm | BuildingFormsDoc | makeHyperbolicUnstableForm | the unstable Grothendieck-Witt class of a hyperbolic form | makeHyperbolicUnstableForm(k)
makeHyperbolicUnstableForm(k, n) | makeHyperbolicUnstableForm(RR, 4) | getSumDecomposition
getSumDecompositionString | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the unstable Grothendieck-Witt class of a hyperbolic form
USAGE: makeHyperbolicUnstableForm(k)
makeHyperbolicUnstableForm(k, n)
INPUTS: k: Ring
a field or finite étale algebra over a field
n: ZZ
an even number, giving an optional rank $n$ for a totally hyperbolic form
OUTPUTS: : UnstableGrothendi... | Key
makeHyperbolicUnstableForm
(makeHyperbolicUnstableForm, Ring)
(makeHyperbolicUnstableForm, Ring, ZZ)
(makeHyperbolicUnstableForm, InexactFieldFamily)
(makeHyperbolicUnstableForm, InexactFieldFamily, ZZ)
Headline
the unstable Grothendieck-Witt class of a hyperbolic form
Usage
makeHyperbolicUnstableFo... | ||
BuildingFormsDoc_a8fd4493_(makeHyperbolicUnstableForm,_Ring) | BuildingFormsDoc | (makeHyperbolicUnstableForm, Ring) | the unstable Grothendieck-Witt class of a hyperbolic form | makeHyperbolicUnstableForm(k)
makeHyperbolicUnstableForm(k, n) | makeHyperbolicUnstableForm(RR, 4) | getSumDecomposition
getSumDecompositionString | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the unstable Grothendieck-Witt class of a hyperbolic form
USAGE: makeHyperbolicUnstableForm(k)
makeHyperbolicUnstableForm(k, n)
INPUTS: k: Ring
a field or finite étale algebra over a field
n: ZZ
an even number, giving an optional rank $n$ for a totally hyperbolic form
OUTPUTS: : UnstableGrothendi... | Key
makeHyperbolicUnstableForm
(makeHyperbolicUnstableForm, Ring)
(makeHyperbolicUnstableForm, Ring, ZZ)
(makeHyperbolicUnstableForm, InexactFieldFamily)
(makeHyperbolicUnstableForm, InexactFieldFamily, ZZ)
Headline
the unstable Grothendieck-Witt class of a hyperbolic form
Usage
makeHyperbolicUnstableFo... | ||
BuildingFormsDoc_a8fd4493_(makeHyperbolicUnstableForm,_Ring,_ZZ) | BuildingFormsDoc | (makeHyperbolicUnstableForm, Ring, ZZ) | the unstable Grothendieck-Witt class of a hyperbolic form | makeHyperbolicUnstableForm(k)
makeHyperbolicUnstableForm(k, n) | makeHyperbolicUnstableForm(RR, 4) | getSumDecomposition
getSumDecompositionString | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the unstable Grothendieck-Witt class of a hyperbolic form
USAGE: makeHyperbolicUnstableForm(k)
makeHyperbolicUnstableForm(k, n)
INPUTS: k: Ring
a field or finite étale algebra over a field
n: ZZ
an even number, giving an optional rank $n$ for a totally hyperbolic form
OUTPUTS: : UnstableGrothendi... | Key
makeHyperbolicUnstableForm
(makeHyperbolicUnstableForm, Ring)
(makeHyperbolicUnstableForm, Ring, ZZ)
(makeHyperbolicUnstableForm, InexactFieldFamily)
(makeHyperbolicUnstableForm, InexactFieldFamily, ZZ)
Headline
the unstable Grothendieck-Witt class of a hyperbolic form
Usage
makeHyperbolicUnstableFo... | ||
BuildingFormsDoc_a8fd4493_(makeHyperbolicUnstableForm,_InexactFieldFamily) | BuildingFormsDoc | (makeHyperbolicUnstableForm, InexactFieldFamily) | the unstable Grothendieck-Witt class of a hyperbolic form | makeHyperbolicUnstableForm(k)
makeHyperbolicUnstableForm(k, n) | makeHyperbolicUnstableForm(RR, 4) | getSumDecomposition
getSumDecompositionString | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the unstable Grothendieck-Witt class of a hyperbolic form
USAGE: makeHyperbolicUnstableForm(k)
makeHyperbolicUnstableForm(k, n)
INPUTS: k: Ring
a field or finite étale algebra over a field
n: ZZ
an even number, giving an optional rank $n$ for a totally hyperbolic form
OUTPUTS: : UnstableGrothendi... | Key
makeHyperbolicUnstableForm
(makeHyperbolicUnstableForm, Ring)
(makeHyperbolicUnstableForm, Ring, ZZ)
(makeHyperbolicUnstableForm, InexactFieldFamily)
(makeHyperbolicUnstableForm, InexactFieldFamily, ZZ)
Headline
the unstable Grothendieck-Witt class of a hyperbolic form
Usage
makeHyperbolicUnstableFo... | ||
BuildingFormsDoc_a8fd4493_(makeHyperbolicUnstableForm,_InexactFieldFamily,_ZZ) | BuildingFormsDoc | (makeHyperbolicUnstableForm, InexactFieldFamily, ZZ) | the unstable Grothendieck-Witt class of a hyperbolic form | makeHyperbolicUnstableForm(k)
makeHyperbolicUnstableForm(k, n) | makeHyperbolicUnstableForm(RR, 4) | getSumDecomposition
getSumDecompositionString | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2 | stable | HEADLINE: the unstable Grothendieck-Witt class of a hyperbolic form
USAGE: makeHyperbolicUnstableForm(k)
makeHyperbolicUnstableForm(k, n)
INPUTS: k: Ring
a field or finite étale algebra over a field
n: ZZ
an even number, giving an optional rank $n$ for a totally hyperbolic form
OUTPUTS: : UnstableGrothendi... | Key
makeHyperbolicUnstableForm
(makeHyperbolicUnstableForm, Ring)
(makeHyperbolicUnstableForm, Ring, ZZ)
(makeHyperbolicUnstableForm, InexactFieldFamily)
(makeHyperbolicUnstableForm, InexactFieldFamily, ZZ)
Headline
the unstable Grothendieck-Witt class of a hyperbolic form
Usage
makeHyperbolicUnstableFo... | ||
DecompositionDoc_b692f3ca_getSumDecomposition | DecompositionDoc | getSumDecomposition | produces a simplified diagonal representative of a Grothendieck-Witt class or unstable Grothendieck-Witt class | getSumDecomposition(beta) | Q = matrix(GF(13), {{9,1,7,4},{1,10,3,2},{7,3,6,7},{4,2,7,5}});
delta = makeGWClass Q;
getSumDecomposition delta | getSumDecompositionString
getAnisotropicPart
getWittIndex | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/DecompositionDoc.m2 | stable | HEADLINE: produces a simplified diagonal representative of a Grothendieck-Witt class or unstable Grothendieck-Witt class
USAGE: getSumDecomposition(beta)
INPUTS: beta: GrothendieckWittClass
over $\mathbb{C},\mathbb{Q},\mathbb{R}$, or a finite field of characteristic not two
beta: UnstableGrothendi... | Key
getSumDecomposition
(getSumDecomposition, GrothendieckWittClass)
(getSumDecomposition, UnstableGrothendieckWittClass)
Headline
produces a simplified diagonal representative of a Grothendieck-Witt class or unstable Grothendieck-Witt class
Usage
getSumDecomposition(beta... | ||
DecompositionDoc_b692f3ca_(getSumDecomposition,_GrothendieckWittClass) | DecompositionDoc | (getSumDecomposition, GrothendieckWittClass) | produces a simplified diagonal representative of a Grothendieck-Witt class or unstable Grothendieck-Witt class | getSumDecomposition(beta) | Q = matrix(GF(13), {{9,1,7,4},{1,10,3,2},{7,3,6,7},{4,2,7,5}});
delta = makeGWClass Q;
getSumDecomposition delta | getSumDecompositionString
getAnisotropicPart
getWittIndex | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/DecompositionDoc.m2 | stable | HEADLINE: produces a simplified diagonal representative of a Grothendieck-Witt class or unstable Grothendieck-Witt class
USAGE: getSumDecomposition(beta)
INPUTS: beta: GrothendieckWittClass
over $\mathbb{C},\mathbb{Q},\mathbb{R}$, or a finite field of characteristic not two
beta: UnstableGrothendi... | Key
getSumDecomposition
(getSumDecomposition, GrothendieckWittClass)
(getSumDecomposition, UnstableGrothendieckWittClass)
Headline
produces a simplified diagonal representative of a Grothendieck-Witt class or unstable Grothendieck-Witt class
Usage
getSumDecomposition(beta... | ||
DecompositionDoc_b692f3ca_(getSumDecomposition,_UnstableGrothendieckWittClass) | DecompositionDoc | (getSumDecomposition, UnstableGrothendieckWittClass) | produces a simplified diagonal representative of a Grothendieck-Witt class or unstable Grothendieck-Witt class | getSumDecomposition(beta) | Q = matrix(GF(13), {{9,1,7,4},{1,10,3,2},{7,3,6,7},{4,2,7,5}});
delta = makeGWClass Q;
getSumDecomposition delta | getSumDecompositionString
getAnisotropicPart
getWittIndex | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/DecompositionDoc.m2 | stable | HEADLINE: produces a simplified diagonal representative of a Grothendieck-Witt class or unstable Grothendieck-Witt class
USAGE: getSumDecomposition(beta)
INPUTS: beta: GrothendieckWittClass
over $\mathbb{C},\mathbb{Q},\mathbb{R}$, or a finite field of characteristic not two
beta: UnstableGrothendi... | Key
getSumDecomposition
(getSumDecomposition, GrothendieckWittClass)
(getSumDecomposition, UnstableGrothendieckWittClass)
Headline
produces a simplified diagonal representative of a Grothendieck-Witt class or unstable Grothendieck-Witt class
Usage
getSumDecomposition(beta... | ||
DecompositionDoc_a0848078_getSumDecompositionString | DecompositionDoc | getSumDecompositionString | produces a simplified string representation of a Grothendieck-Witt class or unstable Grothendieck-Witt class | getSumDecompositionString(beta) | M = matrix(CC, {{1,2,3},{2,4,5},{3,5,6}});
alpha = makeGWClass M;
getSumDecompositionString alpha
N = matrix(RR, {{2.091,2.728,6.747},{2.728,7.329,6.257},{6.747,6.257,0.294}});
beta = makeGWClass N;
getSumDecompositionString beta
P = matrix(QQ, {{1... | getSumDecomposition
getAnisotropicPart
getWittIndex | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/DecompositionDoc.m2 | stable | HEADLINE: produces a simplified string representation of a Grothendieck-Witt class or unstable Grothendieck-Witt class
USAGE: getSumDecompositionString(beta)
INPUTS: beta: GrothendieckWittClass
over $\mathbb{C},\mathbb{Q},\mathbb{R}$, or a finite field of characteristic not two
beta: UnstableGroth... | Key
getSumDecompositionString
(getSumDecompositionString, GrothendieckWittClass)
(getSumDecompositionString, UnstableGrothendieckWittClass)
Headline
produces a simplified string representation of a Grothendieck-Witt class or unstable Grothendieck-Witt class
Usage
getSumDe... | ||
DecompositionDoc_a0848078_(getSumDecompositionString,_GrothendieckWittClass) | DecompositionDoc | (getSumDecompositionString, GrothendieckWittClass) | produces a simplified string representation of a Grothendieck-Witt class or unstable Grothendieck-Witt class | getSumDecompositionString(beta) | M = matrix(CC, {{1,2,3},{2,4,5},{3,5,6}});
alpha = makeGWClass M;
getSumDecompositionString alpha
N = matrix(RR, {{2.091,2.728,6.747},{2.728,7.329,6.257},{6.747,6.257,0.294}});
beta = makeGWClass N;
getSumDecompositionString beta
P = matrix(QQ, {{1... | getSumDecomposition
getAnisotropicPart
getWittIndex | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/DecompositionDoc.m2 | stable | HEADLINE: produces a simplified string representation of a Grothendieck-Witt class or unstable Grothendieck-Witt class
USAGE: getSumDecompositionString(beta)
INPUTS: beta: GrothendieckWittClass
over $\mathbb{C},\mathbb{Q},\mathbb{R}$, or a finite field of characteristic not two
beta: UnstableGroth... | Key
getSumDecompositionString
(getSumDecompositionString, GrothendieckWittClass)
(getSumDecompositionString, UnstableGrothendieckWittClass)
Headline
produces a simplified string representation of a Grothendieck-Witt class or unstable Grothendieck-Witt class
Usage
getSumDe... | ||
DecompositionDoc_a0848078_(getSumDecompositionString,_UnstableGrothendieckWittClass) | DecompositionDoc | (getSumDecompositionString, UnstableGrothendieckWittClass) | produces a simplified string representation of a Grothendieck-Witt class or unstable Grothendieck-Witt class | getSumDecompositionString(beta) | M = matrix(CC, {{1,2,3},{2,4,5},{3,5,6}});
alpha = makeGWClass M;
getSumDecompositionString alpha
N = matrix(RR, {{2.091,2.728,6.747},{2.728,7.329,6.257},{6.747,6.257,0.294}});
beta = makeGWClass N;
getSumDecompositionString beta
P = matrix(QQ, {{1... | getSumDecomposition
getAnisotropicPart
getWittIndex | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/DecompositionDoc.m2 | stable | HEADLINE: produces a simplified string representation of a Grothendieck-Witt class or unstable Grothendieck-Witt class
USAGE: getSumDecompositionString(beta)
INPUTS: beta: GrothendieckWittClass
over $\mathbb{C},\mathbb{Q},\mathbb{R}$, or a finite field of characteristic not two
beta: UnstableGroth... | Key
getSumDecompositionString
(getSumDecompositionString, GrothendieckWittClass)
(getSumDecompositionString, UnstableGrothendieckWittClass)
Headline
produces a simplified string representation of a Grothendieck-Witt class or unstable Grothendieck-Witt class
Usage
getSumDe... | ||
DecompositionDoc_fd9d8d8e_getAnisotropicPart | DecompositionDoc | getAnisotropicPart | produces the anisotropic part of a Grothendieck-Witt class | getAnisotropicPart(beta) | alpha = makeDiagonalForm(QQ, (3,-3,2,5,1,-9));
getAnisotropicPart alpha | getAnisotropicDimension
getWittIndex
getSumDecomposition
getSumDecompositionString | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/DecompositionDoc.m2 | stable | HEADLINE: produces the anisotropic part of a Grothendieck-Witt class
USAGE: getAnisotropicPart(beta)
INPUTS: beta: GrothendieckWittClass
over $\mathbb{C},\mathbb{Q},\mathbb{R}$, or a finite field of characteristic not two
OUTPUTS: : GrothendieckWittClass
the anisotropic part of the Grothendie... | Key
getAnisotropicPart
(getAnisotropicPart, GrothendieckWittClass)
(getAnisotropicPart, Matrix)
Headline
produces the anisotropic part of a Grothendieck-Witt class
Usage
getAnisotropicPart(beta)
Inputs
beta: GrothendieckWittClass
over $\mathbb{C},\... | ||
DecompositionDoc_fd9d8d8e_(getAnisotropicPart,_GrothendieckWittClass) | DecompositionDoc | (getAnisotropicPart, GrothendieckWittClass) | produces the anisotropic part of a Grothendieck-Witt class | getAnisotropicPart(beta) | alpha = makeDiagonalForm(QQ, (3,-3,2,5,1,-9));
getAnisotropicPart alpha | getAnisotropicDimension
getWittIndex
getSumDecomposition
getSumDecompositionString | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/DecompositionDoc.m2 | stable | HEADLINE: produces the anisotropic part of a Grothendieck-Witt class
USAGE: getAnisotropicPart(beta)
INPUTS: beta: GrothendieckWittClass
over $\mathbb{C},\mathbb{Q},\mathbb{R}$, or a finite field of characteristic not two
OUTPUTS: : GrothendieckWittClass
the anisotropic part of the Grothendie... | Key
getAnisotropicPart
(getAnisotropicPart, GrothendieckWittClass)
(getAnisotropicPart, Matrix)
Headline
produces the anisotropic part of a Grothendieck-Witt class
Usage
getAnisotropicPart(beta)
Inputs
beta: GrothendieckWittClass
over $\mathbb{C},\... | ||
DecompositionDoc_fd9d8d8e_(getAnisotropicPart,_Matrix) | DecompositionDoc | (getAnisotropicPart, Matrix) | produces the anisotropic part of a Grothendieck-Witt class | getAnisotropicPart(beta) | alpha = makeDiagonalForm(QQ, (3,-3,2,5,1,-9));
getAnisotropicPart alpha | getAnisotropicDimension
getWittIndex
getSumDecomposition
getSumDecompositionString | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/DecompositionDoc.m2 | stable | HEADLINE: produces the anisotropic part of a Grothendieck-Witt class
USAGE: getAnisotropicPart(beta)
INPUTS: beta: GrothendieckWittClass
over $\mathbb{C},\mathbb{Q},\mathbb{R}$, or a finite field of characteristic not two
OUTPUTS: : GrothendieckWittClass
the anisotropic part of the Grothendie... | Key
getAnisotropicPart
(getAnisotropicPart, GrothendieckWittClass)
(getAnisotropicPart, Matrix)
Headline
produces the anisotropic part of a Grothendieck-Witt class
Usage
getAnisotropicPart(beta)
Inputs
beta: GrothendieckWittClass
over $\mathbb{C},\... | ||
GWInvariantsDoc_9e7c413f_getSignature | GWInvariantsDoc | getSignature | computes the signature of a symmetric bilinear form over the real numbers or rational numbers | getSignature(beta) | M = matrix(RR, {{0,0,1},{0,1,0},{1,0,0}});
beta = makeGWClass M;
getSignature beta | isIsomorphicForm
getHilbertSymbol
getSumDecomposition
getSumDecompositionString | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/GWInvariantsDoc.m2 | stable | HEADLINE: computes the signature of a symmetric bilinear form over the real numbers or rational numbers
USAGE: getSignature(beta)
INPUTS: beta: GrothendieckWittClass
a symmetric bilinear form defined over $\mathbb{Q}$ or $\mathbb{R}$
OUTPUTS: :ZZ
the signature of the symmetric bilinear form $... | Key
getSignature
(getSignature, GrothendieckWittClass)
Headline
computes the signature of a symmetric bilinear form over the real numbers or rational numbers
Usage
getSignature(beta)
Inputs
beta: GrothendieckWittClass
a symmetric bilinear form defined over... | ||
GWInvariantsDoc_9e7c413f_(getSignature,_GrothendieckWittClass) | GWInvariantsDoc | (getSignature, GrothendieckWittClass) | computes the signature of a symmetric bilinear form over the real numbers or rational numbers | getSignature(beta) | M = matrix(RR, {{0,0,1},{0,1,0},{1,0,0}});
beta = makeGWClass M;
getSignature beta | isIsomorphicForm
getHilbertSymbol
getSumDecomposition
getSumDecompositionString | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/GWInvariantsDoc.m2 | stable | HEADLINE: computes the signature of a symmetric bilinear form over the real numbers or rational numbers
USAGE: getSignature(beta)
INPUTS: beta: GrothendieckWittClass
a symmetric bilinear form defined over $\mathbb{Q}$ or $\mathbb{R}$
OUTPUTS: :ZZ
the signature of the symmetric bilinear form $... | Key
getSignature
(getSignature, GrothendieckWittClass)
Headline
computes the signature of a symmetric bilinear form over the real numbers or rational numbers
Usage
getSignature(beta)
Inputs
beta: GrothendieckWittClass
a symmetric bilinear form defined over... | ||
GWInvariantsDoc_e1669443_getIntegralDiscriminant | GWInvariantsDoc | getIntegralDiscriminant | computes the integral discriminant for a rational symmetric bilinear form | getIntegralDiscriminant(beta) | beta = makeGWClass matrix(QQ, {{1,4,7},{4,3,-1},{7,-1,5}});
getIntegralDiscriminant beta
getDiagonalClass beta | isIsomorphicForm | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/GWInvariantsDoc.m2 | stable | HEADLINE: computes the integral discriminant for a rational symmetric bilinear form
USAGE: getIntegralDiscriminant(beta)
INPUTS: beta: GrothendieckWittClass
denoted by $\beta \in \text{GW}(\mathbb{Q})$
OUTPUTS: :ZZ
an integral square class representative of $\text{disc}(\beta)$
EXAMPLE CODE:... | Key
getIntegralDiscriminant
(getIntegralDiscriminant, GrothendieckWittClass)
Headline
computes the integral discriminant for a rational symmetric bilinear form
Usage
getIntegralDiscriminant(beta)
Inputs
beta: GrothendieckWittClass
denoted by $\beta \in ... | ||
GWInvariantsDoc_e1669443_(getIntegralDiscriminant,_GrothendieckWittClass) | GWInvariantsDoc | (getIntegralDiscriminant, GrothendieckWittClass) | computes the integral discriminant for a rational symmetric bilinear form | getIntegralDiscriminant(beta) | beta = makeGWClass matrix(QQ, {{1,4,7},{4,3,-1},{7,-1,5}});
getIntegralDiscriminant beta
getDiagonalClass beta | isIsomorphicForm | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/GWInvariantsDoc.m2 | stable | HEADLINE: computes the integral discriminant for a rational symmetric bilinear form
USAGE: getIntegralDiscriminant(beta)
INPUTS: beta: GrothendieckWittClass
denoted by $\beta \in \text{GW}(\mathbb{Q})$
OUTPUTS: :ZZ
an integral square class representative of $\text{disc}(\beta)$
EXAMPLE CODE:... | Key
getIntegralDiscriminant
(getIntegralDiscriminant, GrothendieckWittClass)
Headline
computes the integral discriminant for a rational symmetric bilinear form
Usage
getIntegralDiscriminant(beta)
Inputs
beta: GrothendieckWittClass
denoted by $\beta \in ... | ||
GWInvariantsDoc_7cd061ac_getHasseWittInvariant | GWInvariantsDoc | getHasseWittInvariant | computes the Hasse-Witt invariant at a prime $p$ for the quadratic form of the Grothendieck-Witt class | getHasseWittInvariant(beta, p) | beta = makeGWClass matrix(QQ, {{1,4,7},{4,3,-1},{7,-1,5}});
getHasseWittInvariant(beta, 7) | isIsomorphicForm
getRelevantPrimes | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/GWInvariantsDoc.m2 | stable | HEADLINE: computes the Hasse-Witt invariant at a prime $p$ for the quadratic form of the Grothendieck-Witt class
USAGE: getHasseWittInvariant(beta, p)
INPUTS: beta: GrothendieckWittClass
denoted by $\beta \in \text{GW}(\mathbb{Q})$
p: ZZ
a prime number
OUTPUTS: :ZZ
the Has... | Key
getHasseWittInvariant
(getHasseWittInvariant, GrothendieckWittClass, ZZ)
(getHasseWittInvariant, List, ZZ)
Headline
computes the Hasse-Witt invariant at a prime $p$ for the quadratic form of the Grothendieck-Witt class
Usage
getHasseWittInvariant(beta, p)
Inputs
... | ||
GWInvariantsDoc_7cd061ac_(getHasseWittInvariant,_GrothendieckWittClass,_ZZ) | GWInvariantsDoc | (getHasseWittInvariant, GrothendieckWittClass, ZZ) | computes the Hasse-Witt invariant at a prime $p$ for the quadratic form of the Grothendieck-Witt class | getHasseWittInvariant(beta, p) | beta = makeGWClass matrix(QQ, {{1,4,7},{4,3,-1},{7,-1,5}});
getHasseWittInvariant(beta, 7) | isIsomorphicForm
getRelevantPrimes | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/GWInvariantsDoc.m2 | stable | HEADLINE: computes the Hasse-Witt invariant at a prime $p$ for the quadratic form of the Grothendieck-Witt class
USAGE: getHasseWittInvariant(beta, p)
INPUTS: beta: GrothendieckWittClass
denoted by $\beta \in \text{GW}(\mathbb{Q})$
p: ZZ
a prime number
OUTPUTS: :ZZ
the Has... | Key
getHasseWittInvariant
(getHasseWittInvariant, GrothendieckWittClass, ZZ)
(getHasseWittInvariant, List, ZZ)
Headline
computes the Hasse-Witt invariant at a prime $p$ for the quadratic form of the Grothendieck-Witt class
Usage
getHasseWittInvariant(beta, p)
Inputs
... | ||
GWInvariantsDoc_7cd061ac_(getHasseWittInvariant,_List,_ZZ) | GWInvariantsDoc | (getHasseWittInvariant, List, ZZ) | computes the Hasse-Witt invariant at a prime $p$ for the quadratic form of the Grothendieck-Witt class | getHasseWittInvariant(beta, p) | beta = makeGWClass matrix(QQ, {{1,4,7},{4,3,-1},{7,-1,5}});
getHasseWittInvariant(beta, 7) | isIsomorphicForm
getRelevantPrimes | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/GWInvariantsDoc.m2 | stable | HEADLINE: computes the Hasse-Witt invariant at a prime $p$ for the quadratic form of the Grothendieck-Witt class
USAGE: getHasseWittInvariant(beta, p)
INPUTS: beta: GrothendieckWittClass
denoted by $\beta \in \text{GW}(\mathbb{Q})$
p: ZZ
a prime number
OUTPUTS: :ZZ
the Has... | Key
getHasseWittInvariant
(getHasseWittInvariant, GrothendieckWittClass, ZZ)
(getHasseWittInvariant, List, ZZ)
Headline
computes the Hasse-Witt invariant at a prime $p$ for the quadratic form of the Grothendieck-Witt class
Usage
getHasseWittInvariant(beta, p)
Inputs
... | ||
GWInvariantsDoc_70bf4a36_getRelevantPrimes | GWInvariantsDoc | getRelevantPrimes | outputs a list containing all primes $p$ where the Hasse-Witt invariant of a symmetric bilinear form is nontrivial | getRelevantPrimes(beta) | beta = makeDiagonalForm(QQ, (6,7,22));
getRelevantPrimes(beta) | getHasseWittInvariant | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/GWInvariantsDoc.m2 | stable | HEADLINE: outputs a list containing all primes $p$ where the Hasse-Witt invariant of a symmetric bilinear form is nontrivial
USAGE: getRelevantPrimes(beta)
INPUTS: beta: GrothendieckWittClass
denoted by $\beta \in \text{GW}(\mathbb{Q})$
OUTPUTS: : List
a finite list of primes $(p_1,\ldots,p_r... | Key
getRelevantPrimes
(getRelevantPrimes, GrothendieckWittClass)
Headline
outputs a list containing all primes $p$ where the Hasse-Witt invariant of a symmetric bilinear form is nontrivial
Usage
getRelevantPrimes(beta)
Inputs
beta: GrothendieckWittClass
de... | ||
GWInvariantsDoc_70bf4a36_(getRelevantPrimes,_GrothendieckWittClass) | GWInvariantsDoc | (getRelevantPrimes, GrothendieckWittClass) | outputs a list containing all primes $p$ where the Hasse-Witt invariant of a symmetric bilinear form is nontrivial | getRelevantPrimes(beta) | beta = makeDiagonalForm(QQ, (6,7,22));
getRelevantPrimes(beta) | getHasseWittInvariant | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/GWInvariantsDoc.m2 | stable | HEADLINE: outputs a list containing all primes $p$ where the Hasse-Witt invariant of a symmetric bilinear form is nontrivial
USAGE: getRelevantPrimes(beta)
INPUTS: beta: GrothendieckWittClass
denoted by $\beta \in \text{GW}(\mathbb{Q})$
OUTPUTS: : List
a finite list of primes $(p_1,\ldots,p_r... | Key
getRelevantPrimes
(getRelevantPrimes, GrothendieckWittClass)
Headline
outputs a list containing all primes $p$ where the Hasse-Witt invariant of a symmetric bilinear form is nontrivial
Usage
getRelevantPrimes(beta)
Inputs
beta: GrothendieckWittClass
de... | ||
GWInvariantsDoc_a5ce035c_getRank | GWInvariantsDoc | getRank | calculates the rank of a symmetric bilinear form | getRank(beta) | beta = makeDiagonalForm(QQ, (3,5,7,11))
getRank beta | isIsomorphicForm
getSignature | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/GWInvariantsDoc.m2 | stable | HEADLINE: calculates the rank of a symmetric bilinear form
USAGE: getRank(beta)
INPUTS: beta: GrothendieckWittClass
a symmetric bilinear form defined over $\mathbb{Q}$
OUTPUTS: : ZZ
the rank of the symmetric bilinear form $\beta$
EXAMPLE CODE:
```macaulay2
beta = makeDiagonalForm(QQ, (3,5,7,... | Key
getRank
(getRank, GrothendieckWittClass)
(getRank, Matrix)
Headline
calculates the rank of a symmetric bilinear form
Usage
getRank(beta)
Inputs
beta: GrothendieckWittClass
a symmetric bilinear form defined over $\mathbb{Q}$
Outputs
... | ||
GWInvariantsDoc_a5ce035c_(getRank,_GrothendieckWittClass) | GWInvariantsDoc | (getRank, GrothendieckWittClass) | calculates the rank of a symmetric bilinear form | getRank(beta) | beta = makeDiagonalForm(QQ, (3,5,7,11))
getRank beta | isIsomorphicForm
getSignature | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/GWInvariantsDoc.m2 | stable | HEADLINE: calculates the rank of a symmetric bilinear form
USAGE: getRank(beta)
INPUTS: beta: GrothendieckWittClass
a symmetric bilinear form defined over $\mathbb{Q}$
OUTPUTS: : ZZ
the rank of the symmetric bilinear form $\beta$
EXAMPLE CODE:
```macaulay2
beta = makeDiagonalForm(QQ, (3,5,7,... | Key
getRank
(getRank, GrothendieckWittClass)
(getRank, Matrix)
Headline
calculates the rank of a symmetric bilinear form
Usage
getRank(beta)
Inputs
beta: GrothendieckWittClass
a symmetric bilinear form defined over $\mathbb{Q}$
Outputs
... | ||
GWInvariantsDoc_a5ce035c_(getRank,_Matrix) | GWInvariantsDoc | (getRank, Matrix) | calculates the rank of a symmetric bilinear form | getRank(beta) | beta = makeDiagonalForm(QQ, (3,5,7,11))
getRank beta | isIsomorphicForm
getSignature | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/GWInvariantsDoc.m2 | stable | HEADLINE: calculates the rank of a symmetric bilinear form
USAGE: getRank(beta)
INPUTS: beta: GrothendieckWittClass
a symmetric bilinear form defined over $\mathbb{Q}$
OUTPUTS: : ZZ
the rank of the symmetric bilinear form $\beta$
EXAMPLE CODE:
```macaulay2
beta = makeDiagonalForm(QQ, (3,5,7,... | Key
getRank
(getRank, GrothendieckWittClass)
(getRank, Matrix)
Headline
calculates the rank of a symmetric bilinear form
Usage
getRank(beta)
Inputs
beta: GrothendieckWittClass
a symmetric bilinear form defined over $\mathbb{Q}$
Outputs
... | ||
GWTransferDoc_8af37dc3_transferGW | GWTransferDoc | transferGW | the transfer of Grothendieck-Witt from an étale algebras to a base field | transferGW(beta) | R = QQ[x]/(x^2 - 1);
beta = makeGWClass matrix(R, {{1,2},{2,x}});
transferGW(beta) | GrothendieckWittClass
getTrace | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/GWTransferDoc.m2 | stable | HEADLINE: the transfer of Grothendieck-Witt from an étale algebras to a base field
USAGE: transferGW(beta)
INPUTS: beta: GrothendieckWittClass
Grothendieck-Witt class over an étale algebra over field of characteristic not 2
OUTPUTS: : GrothendieckWittClass
the image of the Grothendieck-Witt class beta in $\tex... | Key
transferGW
(transferGW, GrothendieckWittClass)
Headline
the transfer of Grothendieck-Witt from an étale algebras to a base field
Usage
transferGW(beta)
Inputs
beta: GrothendieckWittClass
Grothendieck-Witt class over an étale algebra over field of characteristic not 2
Outputs
: GrothendieckWittCla... | ||
GWTransferDoc_8af37dc3_(transferGW,_GrothendieckWittClass) | GWTransferDoc | (transferGW, GrothendieckWittClass) | the transfer of Grothendieck-Witt from an étale algebras to a base field | transferGW(beta) | R = QQ[x]/(x^2 - 1);
beta = makeGWClass matrix(R, {{1,2},{2,x}});
transferGW(beta) | GrothendieckWittClass
getTrace | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/GWTransferDoc.m2 | stable | HEADLINE: the transfer of Grothendieck-Witt from an étale algebras to a base field
USAGE: transferGW(beta)
INPUTS: beta: GrothendieckWittClass
Grothendieck-Witt class over an étale algebra over field of characteristic not 2
OUTPUTS: : GrothendieckWittClass
the image of the Grothendieck-Witt class beta in $\tex... | Key
transferGW
(transferGW, GrothendieckWittClass)
Headline
the transfer of Grothendieck-Witt from an étale algebras to a base field
Usage
transferGW(beta)
Inputs
beta: GrothendieckWittClass
Grothendieck-Witt class over an étale algebra over field of characteristic not 2
Outputs
: GrothendieckWittCla... | ||
GrothendieckWittClassesDoc_2478be61_GrothendieckWittClass | GrothendieckWittClassesDoc | GrothendieckWittClass | a new type intended to capture the isomorphism class of an element of the Grothendieck-Witt ring of a field or finite étale algebras over a field | diagonalClass = getDiagonalClass beta;
beta.cache.getDiagonalClass | makeGWClass
getAlgebra
getBaseField
getMatrix
getDiagonalClass | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/GrothendieckWittClassesDoc.m2 | stable | HEADLINE: a new type intended to capture the isomorphism class of an element of the Grothendieck-Witt ring of a field or finite étale algebras over a field
EXAMPLE CODE:
```macaulay2
diagonalClass = getDiagonalClass beta;
beta.cache.getDiagonalClass
```
SEEALSO: makeGWClass
getAlgebra
getBaseField
getMatrix
... | Key
GrothendieckWittClass
(net, GrothendieckWittClass)
(texMath, GrothendieckWittClass)
Headline
a new type intended to capture the isomorphism class of an element of the Grothendieck-Witt ring of a field or finite étale algebras over a field
Description
Text
A @TT("GrothendieckWittClass")@ object is a ... | |||
GrothendieckWittClassesDoc_2478be61_(net,_GrothendieckWittClass) | GrothendieckWittClassesDoc | (net, GrothendieckWittClass) | a new type intended to capture the isomorphism class of an element of the Grothendieck-Witt ring of a field or finite étale algebras over a field | diagonalClass = getDiagonalClass beta;
beta.cache.getDiagonalClass | makeGWClass
getAlgebra
getBaseField
getMatrix
getDiagonalClass | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/GrothendieckWittClassesDoc.m2 | stable | HEADLINE: a new type intended to capture the isomorphism class of an element of the Grothendieck-Witt ring of a field or finite étale algebras over a field
EXAMPLE CODE:
```macaulay2
diagonalClass = getDiagonalClass beta;
beta.cache.getDiagonalClass
```
SEEALSO: makeGWClass
getAlgebra
getBaseField
getMatrix
... | Key
GrothendieckWittClass
(net, GrothendieckWittClass)
(texMath, GrothendieckWittClass)
Headline
a new type intended to capture the isomorphism class of an element of the Grothendieck-Witt ring of a field or finite étale algebras over a field
Description
Text
A @TT("GrothendieckWittClass")@ object is a ... | |||
GrothendieckWittClassesDoc_2478be61_(texMath,_GrothendieckWittClass) | GrothendieckWittClassesDoc | (texMath, GrothendieckWittClass) | a new type intended to capture the isomorphism class of an element of the Grothendieck-Witt ring of a field or finite étale algebras over a field | diagonalClass = getDiagonalClass beta;
beta.cache.getDiagonalClass | makeGWClass
getAlgebra
getBaseField
getMatrix
getDiagonalClass | M2_git/M2/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/GrothendieckWittClassesDoc.m2 | stable | HEADLINE: a new type intended to capture the isomorphism class of an element of the Grothendieck-Witt ring of a field or finite étale algebras over a field
EXAMPLE CODE:
```macaulay2
diagonalClass = getDiagonalClass beta;
beta.cache.getDiagonalClass
```
SEEALSO: makeGWClass
getAlgebra
getBaseField
getMatrix
... | Key
GrothendieckWittClass
(net, GrothendieckWittClass)
(texMath, GrothendieckWittClass)
Headline
a new type intended to capture the isomorphism class of an element of the Grothendieck-Witt ring of a field or finite étale algebras over a field
Description
Text
A @TT("GrothendieckWittClass")@ object is a ... |
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Macaulay2 RAG Chunks
A comprehensive knowledge base extracted directly from the official Macaulay2 source code and documentation packages (M2/Macaulay2/packages). Designed to be ingested into Vector Databases (e.g., ChromaDB, FAISS) for Retrieval-Augmented Generation (RAG).
📊 Dataset Statistics
- Total Chunks: 15,711
- Size: ~45MB
- Code Density: ~85% of chunks contain executable Macaulay2 examples.
- Source: Parsed from 2,208
.m2files using a custom AST/Regex-aware parser (https://gitlab.com/frupniew/llm_macaulay/src/extract_m2_docs_v2.py) that groups documentation per mathematical symbol.
🏷️ Metadata & Filtering
Each chunk is enriched with metadata to allow for highly targeted retrieval:
{
"id": "chunk_8492",
"symbol": "primaryDecomposition",
"package": "PrimaryDecomposition",
"has_code": true,
"headline": "compute the primary decomposition of an ideal",
"usage": "primaryDecomposition I",
"example_code": "R = QQ[x,y,z]; I = ideal(x^2, x*y); primaryDecomposition I"
}
This structure allows RAG pipelines to filter out purely theoretical text when the user explicitly asks for code implementation, or filter by specific algebraic packages (e.g., Schubert2).
🧩 Recommended Embedding Model
Tested and optimized with sentence-transformers/all-MiniLM-L6-v2 for a balance of semantic mathematical understanding and low-latency retrieval.
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