Sample expressions: and All other exponents (including integers with a decimal point, such as 2.0) Speech: [base] raised to the [exponent] power Sample expressions: and Nested exponents (expressions containing exponents that contain exponents) Exponent is of the form , , , or , where the entry is one of the following: A number (integer or decimal) A fraction spoken as ordinal* A variable Speech: [base] raised to the [exponent] power Sample expressions: and Exponent is of the form , , , or , where the entry is one of the following: A number (integer or decimal) A fraction spoken as ordinal* *either by fraction_ordinal preference or by the default Speech: [base] raised to the [exponent] power Sample expressions: and Exponent is of any other form Speech: [base] raised to the exponent [exponent] end exponent Sample expressions: and Note: The fraction spoken as an ordinal is “one-third”, and the fraction spoken as an ordinal is “three-fourths”. Note: If the exponent in the exponent is a 2, the 2 speaks as “squared”. If the exponent in the exponent is a 3, the 3 speaks as “cubed”. Preferences: Ordinal (Exponent_ Ordinal.eqp) All positive integer exponents and exponents that are single letters Speech: [base] to the [exponent-ordinal]
Sample expressions: and Cube roots Speech: the cube root of [expression under square root sign] Sample expressions: and Higher roots with numeric index Speech: the [index ordinal] root of [expression under root sign] Sample expressions: and Higher roots with letter index Speech: the ordinal] root of [expression under root sign] Sample expressions: and Preferences: PosNegSqRoot (Roots_PosNegSqRoot.eqp) Speech: The positive square root of [expression under root sign] Sample expressions: and Speech: The negative square root of [expression under root sign] Sample expressions: and The speech for higher-order roots follows the rules. RootEnd (Roots_RootEnd.eqp) Speech: As indicated in the rules, but “end root” is spoken after the expression under the root sign. Sample expressions: and PosNegSqRootEnd (Roots_PosNegSqRootEnd.eqp) Speech: As indicated in the PosNegSqRoot preference, but “end root” is spoken after the expression under the square root sign. Sample expressions: and
Hyperbolic trigonometric functions Speech: the hyperbolic sine of x Speech: the hyperbolic cosine of x Speech: the hyperbolic tangent of x Speech: the hyperbolic secant of x Speech: the hyperbolic cosecant of x Speech: the hyperbolic cotangent of x Speech: the inverse hyperbolic sine of x Speech: the inverse hyperbolic cosine of x Speech: the inverse hyperbolic tangent of x Speech: the inverse hyperbolic cosecant of x Speech: the inverse hyperbolic secant of x Speech: the inverse hyperbolic cotangent of x Preferences: Note: Trigonometry preferences are only defined for the inverse trigonometric functions. The speech for all other trigonometric functions continues to follow the trigonometry speech rules. TrigInverse (Trig_TrigInverse.eqp) Speech: sine inverse of x Speech: cosine inverse of x Speech: tangent inverse of x Speech: cosecant inverse of x
Speech: the log of, open paren, x plus y, close paren The function Speech: the log, base b, of x Speech: the log, base b, of, open x plus y, close paren The ln function Speech: l n x Speech: l n of, open paren, x plus y, close paren Preference: LnAsNaturalLog (Log_LnAsNaturalLog.eqp) The log function (speech is the same as for the Argument is (see p. 11) Speech: log x All arguments Speech: the log of, open paren, x plus y, close paren The function (speech is the same as for the Speech: the log, base b, of x Speech: the log, base b, of, open paren, x plus y, close paren The ln function Speech: natural log x Speech: the natural log of, open paren, x plus y, close paren Implied Times Some Preliminary Remarks Sometimes expressions of the form entry1(entry2) or entry1[entry1] represent products, and sometimes they represent functions. Therefore, both the ImpliedTimes and Functions rules and preferences could apply to such expressions. The speech for such expressions is determined as follows.
Note: Brackets speak as “open bracket…close bracket”, whether they are nested within another pair of brackets or not. Silent (Paren_Silent.eqp) No parentheses or brackets speak. Sample expressions: and If implied times is not speaking (i.e., the preference is set), then this preference will speak all parentheses and brackets except parentheses and brackets around matrices. Sample expression: CoordPoint (Paren_CoordPoint.eqp) Speech: The point with coordinates, [first coordinate] comma . . . [last coordinate] Sample expressions: and Interval (Paren_Interval.eqp) In the following speech, c and d are used as examples of the speech patterns. Speech: The interval from c to d, not including c or d Speech: The interval from c to d, including c, but not including d Speech: The interval from c to d, not including c, but including d Speech: The interval from c to d, including c and d Speech: The interval from negative infinity to d, not including d Speech: The interval from negative infinity to d, including d Speech: The interval from c to infinity, not including d Speech: The interval from c to infinity, including d Speech: The interval from negative infinity to infinity Speech: The interval from negative infinity to positive infinity Matrices, Vectors, and Combinatorics Rule: (Matrix_Auto.eqp) matrices, where n is less than or equal to 3 and all of whose entries are (see p.11)
Speech: The 1 by [number of columns] row matrix, [entries in row 1]. For example, matrices, all of whose entries are simple expressions, speak as follows. Speech: The 1 by 3 row matrix. [entry], [entry], [entry]. Sample expression: All other matrices Speech: The 1 by [number of columns] row matrix, Column 1: [entry], Column 2 [entry], etc. Sample expressions: and matrices, where n is less than or equal to 3 and all of whose entries are simple expressions Speech: The [number of rows] by 1 matrix, Column 1: [entries in column 1], etc. For example, matrices, all of whose entries are simple expressions speak as follows. Speech: The 3 by 1 column matrix, [entry], [entry], [entry]. Sample expression: All other matrices Speech: The [number of rows] by 1 column matrix, Row 1: [entry], Row 2 [entry], etc. Sample expressions: and matrices, m is equal to 2 or 3 and n is equal to 2 or 3 and all of the entries are simple expressions Speech: The [number of rows] by [number of columns] matrix, Row 1: [entries in row 1], etc. For example, matrices, all of the entries are simple expressions, speak as follows.
Sets enclosed in set brackets { } Rule: (Sets_Auto.eqp) There is either a single vertical bar or a colon in the set. Speech: The set of all [entry between left set bracket and vertical bar] such that [entry between vertical bar and right set bracket] Sample expressions: and is no vertical bar in the set. Speech: The set [entry 1] comma [entry 2] comma . . . Sample expression: is nothing in between the set brackets. Speech: The empty set Sample expression: Preferences: (Sets_woAll.eqp) There is either a single vertical bar or a colon in the set. Speech: The set of [entry between left set bracket and vertical bar] such that [entry between vertical bar and right set bracket]. Sample expressions: and is no vertical bar in the set. (Speech follows the rule) Speech: The set [entry 1] comma [entry 2] comma . . . Sample expression: There is nothing in between the set brackets. (Speech follows the rule) Speech: The set Sample expression: SilentBracket (Sets_SilentBracket.eqp) There is either a single vertical bar or a colon in the set. (Speech follows the rule) Speech: The set of all [entry between left set bracket and vertical bar] such that [entry between vertical bar and right set bracket]. Sample expressions: and is no vertical bar in the set. Speech: [entry1] comma [entry 2] comma . . . Sample expression: There is nothing in between the set brackets. (Speech follows the rule) Speech: The empty set Sample expression:
Part 2: Symbols Multiplication Symbol Rule: (MultSymbolX_Auto.eqp) Speech: times Sample expression: Preference: By (MultSymbolX_By.eqp) Speech: by Sample expression: By (MultSymbolX_Cross.eqp) Speech: cross Sample expression: Multiplication Symbol Rule: (MultSymbolDot_Auto.eqp) Speech: times Sample expression: Preference: By (MultSymbolDot_Dot.eqp) Speech: dot Sample expression:
Set Membership Symbols: and Rule: (SetMemberSymbol_Auto.eqp) The set membership symbol is inside set brackets. Speech: in not in Sample expressions: and The set membership symbol is in an expression below one of the following symbols. Speech: over b is a member of S over b is not a member of S Sample expression: Note: The speech for the symbolsis given in the (Sums, Products, Unions, Intersections, and Integrals; see p. 54). The set membership symbol is not inside set brackets. Speech: is a member of is not a member of Sample expressions: and Preferences: Member (SetMemberSymbol_Member.eqp) The set membership symbol is inside set brackets. Speech: member of not a member of Sample expressions:and The set membership symbol is in an expression below one of the following symbols.
Speech: over b is a member of S over b is not a member of S Sample expression: The set membership symbol is not inside set brackets. Speech: is a member of is not a member of Sample expressions: and Element (SetMemberSymbol_Element.eqp) The set membership symbol is inside set brackets. Speech: element of not an element of Sample expressions:and The set membership symbol is in an expression one of the following symbols. Speech: over b is an element of S over b is not an element of S Sample expression: The set membership symbol is not inside set brackets. Speech: is an element of is not an element of Sample expressions: and In (SetMemberSymbol_In.eqp) The set membership symbol is inside set brackets. Speech: in not in Sample expressions:and The set membership symbol is in an expression below one of the following symbols. Speech: over b is in S over b is not S
Sample expression: The set membership symbol is not inside set brackets. Speech: is in is not in Sample expressions: and Belongs (SetMemberSymbol_Belongs.eqp) The set membership symbol is inside set brackets. Speech: belonging to not belonging to Sample expressions: and The set membership symbol is in an expression below one of the following symbols. Speech: b belongs to S b does not belong to S Sample expression: The set membership symbol is not inside set brackets. Speech: belongs to does not belong to Sample expressions: and Sums, Products, Unions, Intersections, and Integrals Rule: Symbols alone Speech: the sum of Sample expression: Speech: the product of
Sample expression: Speech: the integral Sample expression: Speech: union Sample expression: Speech: union Sample expression: Speech: intersection Sample expression: Speech: intersection Sample expression: Speech: the integral Sample expression: is an entry above and below the symbol. Speech: the sum from [entry below symbol] to [entry above symbol] of [term] Sample expression: Speech: the product from [entry below symbol] to [entry above symbol] of [term] Sample expression:
Conjugate (Bar_Conjugate.eqp) Bar is over digits at the end of a decimal number. Speech: same as the rules Sample expressions: and Otherwise Speech: the complex conjugate of [expression bar] Sample expressions: and Mean (Bar_Mean.eqp) Bar is over digits at the end of a decimal number. Speech: same as the rules Sample expressions: and Otherwise Speech: the mean of [expression under bar] Sample expression: Equals Sign with Adornments Rule: Speech: is defined to be Sample expression: Speech: equals sign with question mark over it Sample expression: