Repository: sympy/sympy

Issue:
Nonlinsolve fails when subsystem gives an ImageSet
```
In [3]: nonlinsolve([x+y, sin(y)], [x, y])                                                                                        
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-3-0183c333f94f> in <module>
----> 1 nonlinsolve([x+y, sin(y)], [x, y])

~/current/sympy/sympy/sympy/solvers/solveset.py in nonlinsolve(system, *symbols)
   3420         # If all the equations are not polynomial.
   3421         # Use `substitution` method for the system
-> 3422         result = substitution(
   3423             polys_expr + nonpolys, symbols, exclude=denominators)
   3424         return result

~/current/sympy/sympy/sympy/solvers/solveset.py in substitution(system, symbols, result, known_symbols, exclude, all_symbols)
   3085     # end def _solve_using_know_values()
   3086 
-> 3087     new_result_real, solve_call1, cnd_call1 = _solve_using_known_values(
   3088         old_result, solveset_real)
   3089     new_result_complex, solve_call2, cnd_call2 = _solve_using_known_values(

~/current/sympy/sympy/sympy/solvers/solveset.py in _solve_using_known_values(result, solver)
   3001                     not_solvable = False
   3002                     try:
-> 3003                         soln = solver(eq2, sym)
   3004                         total_solvest_call += 1
   3005                         soln_new = S.EmptySet

~/current/sympy/sympy/sympy/solvers/solveset.py in solveset_real(f, symbol)
   2036 
   2037 def solveset_real(f, symbol):
-> 2038     return solveset(f, symbol, S.Reals)
   2039 
   2040 

~/current/sympy/sympy/sympy/solvers/solveset.py in solveset(f, symbol, domain)
   2014             try:
   2015                 r = Dummy('r', **assumptions)
-> 2016                 return solveset(f.xreplace({symbol: r}), r, domain
   2017                     ).xreplace({r: symbol})
   2018             except InconsistentAssumptions:

~/current/sympy/sympy/sympy/solvers/solveset.py in solveset(f, symbol, domain)
   2032     f = piecewise_fold(f)
   2033 
-> 2034     return _solveset(f, symbol, domain, _check=True)
   2035 
   2036 

~/current/sympy/sympy/sympy/solvers/solveset.py in _solveset(f, symbol, domain, _check)
    905         if m not in set([S.ComplexInfinity, S.Zero, S.Infinity,
    906                               S.NegativeInfinity]):
--> 907             f = a/m + h  # XXX condition `m != 0` should be added to soln
    908 
    909     # assign the solvers to use

TypeError: unsupported operand type(s) for /: 'ImageSet' and 'One'
```

Discussion:
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Hi, I am the [SymPy bot](https://github.com/sympy/sympy-bot) (v161). I'm here to help you write a release notes entry. Please read the [guide on how to write release notes](https://github.com/sympy/sympy/wiki/Writing-Release-Notes).



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<details><summary>Click here to see the pull request description that was parsed.</summary>

    Removed Attribute error, type error from `nonlinsolve`, which was due to `imageset` as it was not parsed properly in right place.

    Closes #19050
    Closes #16618
    <!-- BEGIN RELEASE NOTES -->
    NO ENTRY
    <!-- END RELEASE NOTES -->

</details><p>

smichr: > # have to remove the redundancy

Let's see if that can be fixed before committing this. Are those different `n` values? If not, I don't know how they exist simultaneously in FiniteSet.  Also, consider using `soln` and `ans` for the result of the call to the solver. Calling it `eq` is counter-intuitive. And you should probably be checking the output solution, not `ans` since you can see that the tests are trivially true for what you defined.
MaqOwais: > have to remove the redundancy

If we do this successfully then more 2 issues will also be closed https://github.com/sympy/sympy/issues/14565 , https://github.com/sympy/sympy/issues/13961 simultaneously : )


>  If not, I don't know how they exist simultaneously in FiniteSet. 

Yep that is the reason `assert len(eq) == 8 # == len(ans)` ( in diff) was not working as it was showing 4 instead of 8. But it's giving the output with 8 tuples in `FiniteSet`.

Patch:
diff --git a/doc/src/modules/polys/domainmatrix.rst b/doc/src/modules/polys/domainmatrix.rst
index 0561b3dc9e..ffb33518f3 100644
--- a/doc/src/modules/polys/domainmatrix.rst
+++ b/doc/src/modules/polys/domainmatrix.rst
@@ -46,10 +46,3 @@ DDM Class Reference
 
 .. autoclass:: DDM
    :members:
-
-SDM Class Reference
-===================
-.. currentmodule:: sympy.polys.matrices.sdm
-
-.. autoclass:: SDM
-   :members:
diff --git a/sympy/functions/elementary/piecewise.py b/sympy/functions/elementary/piecewise.py
index 377c7cafbc..b986d9840f 100644
--- a/sympy/functions/elementary/piecewise.py
+++ b/sympy/functions/elementary/piecewise.py
@@ -742,39 +742,16 @@ def nonsymfail(cond):
             if isinstance(cond, And):
                 lower = S.NegativeInfinity
                 upper = S.Infinity
-                exclude = []
                 for cond2 in cond.args:
                     if isinstance(cond2, Equality):
                         lower = upper  # ignore
                         break
-                    elif isinstance(cond2, Unequality):
-                        l, r = cond2.args
-                        if l == sym:
-                            exclude.append(r)
-                        elif r == sym:
-                            exclude.append(l)
-                        else:
-                            nonsymfail(cond2)
-                        continue
                     elif cond2.lts == sym:
                         upper = Min(cond2.gts, upper)
                     elif cond2.gts == sym:
                         lower = Max(cond2.lts, lower)
                     else:
                         nonsymfail(cond2)  # should never get here
-                if exclude:
-                    exclude = list(ordered(exclude))
-                    newcond = []
-                    for i, e in enumerate(exclude):
-                        if e < lower == True or e > upper == True:
-                            continue
-                        if not newcond:
-                            newcond.append((None, lower))  # add a primer
-                        newcond.append((newcond[-1][1], e))
-                    newcond.append((newcond[-1][1], upper))
-                    newcond.pop(0)  # remove the primer
-                    expr_cond.extend([(iarg, expr, And(i[0] < sym, sym < i[1])) for i in newcond])
-                    continue
             elif isinstance(cond, Relational):
                 lower, upper = cond.lts, cond.gts  # part 1: initialize with givens
                 if cond.lts == sym:                # part 1a: expand the side ...
diff --git a/sympy/geometry/ellipse.py b/sympy/geometry/ellipse.py
index d01182a3cd..aedefd518b 100644
--- a/sympy/geometry/ellipse.py
+++ b/sympy/geometry/ellipse.py
@@ -1307,11 +1307,9 @@ def tangent_lines(self, p):
 
             # handle horizontal and vertical tangent lines
             if len(tangent_points) == 1:
-                if tangent_points[0][
-                           0] == p.x or tangent_points[0][1] == p.y:
-                    return [Line(p, p + Point(1, 0)), Line(p, p + Point(0, 1))]
-                else:
-                    return [Line(p, p + Point(0, 1)), Line(p, tangent_points[0])]
+                assert tangent_points[0][
+                           0] == p.x or tangent_points[0][1] == p.y
+                return [Line(p, p + Point(1, 0)), Line(p, p + Point(0, 1))]
 
             # others
             return [Line(p, tangent_points[0]), Line(p, tangent_points[1])]
diff --git a/sympy/integrals/transforms.py b/sympy/integrals/transforms.py
index 4c6dffef9d..57a786fd45 100644
--- a/sympy/integrals/transforms.py
+++ b/sympy/integrals/transforms.py
@@ -2,7 +2,7 @@
 from functools import reduce
 
 from sympy.core import S
-from sympy.core.compatibility import iterable, ordered
+from sympy.core.compatibility import iterable
 from sympy.core.function import Function
 from sympy.core.relational import _canonical, Ge, Gt
 from sympy.core.numbers import oo
@@ -1084,13 +1084,13 @@ def process_conds(conds):
                 a = Max(a_, a)
             else:
                 aux = And(aux, Or(*aux_))
-        return a, aux.canonical if aux.is_Relational else aux
+        return a, aux
 
     conds = [process_conds(c) for c in disjuncts(cond)]
     conds2 = [x for x in conds if x[1] != False and x[0] != -oo]
     if not conds2:
         conds2 = [x for x in conds if x[1] != False]
-    conds = list(ordered(conds2))
+    conds = conds2
 
     def cnt(expr):
         if expr == True or expr == False:
@@ -1100,7 +1100,7 @@ def cnt(expr):
 
     if not conds:
         raise IntegralTransformError('Laplace', f, 'no convergence found')
-    a, aux = conds[0]  # XXX is [0] always the right one?
+    a, aux = conds[0]
 
     def sbs(expr):
         return expr.subs(s, s_)
diff --git a/sympy/matrices/expressions/matexpr.py b/sympy/matrices/expressions/matexpr.py
index e11946015c..6dc87b5754 100644
--- a/sympy/matrices/expressions/matexpr.py
+++ b/sympy/matrices/expressions/matexpr.py
@@ -653,7 +653,7 @@ def _matrix_derivative(expr, x):
 
     from sympy.tensor.array.expressions.conv_array_to_matrix import convert_array_to_matrix
 
-    parts = [[convert_array_to_matrix(j) for j in i] for i in parts]
+    parts = [[convert_array_to_matrix(j).doit() for j in i] for i in parts]
 
     def _get_shape(elem):
         if isinstance(elem, MatrixExpr):
@@ -897,7 +897,7 @@ def build(self):
         data = [self._build(i) for i in self._lines]
         if self.higher != 1:
             data += [self._build(self.higher)]
-        data = [i for i in data]
+        data = [i.doit() for i in data]
         return data
 
     def matrix_form(self):
diff --git a/sympy/polys/matrices/ddm.py b/sympy/polys/matrices/ddm.py
index 84ab1712f8..bf244373ea 100644
--- a/sympy/polys/matrices/ddm.py
+++ b/sympy/polys/matrices/ddm.py
@@ -84,9 +84,6 @@ class DDM(list):
     This is a list subclass and is a wrapper for a list of lists that supports
     basic matrix arithmetic +, -, *, **.
     """
-
-    fmt = 'dense'
-
     def __init__(self, rowslist, shape, domain):
         super().__init__(rowslist)
         self.shape = self.rows, self.cols = m, n = shape
@@ -95,29 +92,9 @@ def __init__(self, rowslist, shape, domain):
         if not (len(self) == m and all(len(row) == n for row in self)):
             raise DDMBadInputError("Inconsistent row-list/shape")
 
-    def to_list(self):
-        return list(self)
-
-    def to_ddm(self):
-        return self
-
-    def to_sdm(self):
-        return SDM.from_list(self, self.shape, self.domain)
-
-    def convert_to(self, K):
-        Kold = self.domain
-        if K == Kold:
-            return self.copy()
-        rows = ([K.convert_from(e, Kold) for e in row] for row in self)
-        return DDM(rows, self.shape, K)
-
     def __str__(self):
-        rowsstr = ['[%s]' % ', '.join(map(str, row)) for row in self]
-        return '[%s]' % ', '.join(rowsstr)
-
-    def __repr__(self):
         cls = type(self).__name__
-        rows = list.__repr__(self)
+        rows = list.__str__(self)
         return '%s(%s, %s, %s)' % (cls, rows, self.shape, self.domain)
 
     def __eq__(self, other):
@@ -221,22 +198,6 @@ def matmul(a, b):
         ddm_imatmul(c, a, b)
         return c
 
-    def hstack(A, B):
-        Anew = list(A.copy())
-        rows, cols = A.shape
-        domain = A.domain
-
-        Brows, Bcols = B.shape
-        assert Brows == rows
-        assert B.domain == domain
-
-        cols += Bcols
-
-        for i, Bi in enumerate(B):
-            Anew[i].extend(Bi)
-
-        return DDM(Anew, (rows, cols), A.domain)
-
     def rref(a):
         """Reduced-row echelon form of a and list of pivots"""
         b = a.copy()
@@ -249,17 +210,15 @@ def nullspace(a):
         domain = a.domain
 
         basis = []
-        nonpivots = []
         for i in range(cols):
             if i in pivots:
                 continue
-            nonpivots.append(i)
             vec = [domain.one if i == j else domain.zero for j in range(cols)]
             for ii, jj in enumerate(pivots):
                 vec[jj] -= rref[ii][i]
             basis.append(vec)
 
-        return DDM(basis, (len(basis), cols), domain), nonpivots
+        return DDM(basis, (len(basis), cols), domain)
 
     def det(a):
         """Determinant of a"""
@@ -312,6 +271,3 @@ def charpoly(a):
         vec = ddm_berk(a, K)
         coeffs = [vec[i][0] for i in range(n+1)]
         return coeffs
-
-
-from .sdm import SDM
diff --git a/sympy/polys/matrices/domainmatrix.py b/sympy/polys/matrices/domainmatrix.py
index cb073e2bad..65c090719b 100644
--- a/sympy/polys/matrices/domainmatrix.py
+++ b/sympy/polys/matrices/domainmatrix.py
@@ -13,8 +13,7 @@
 
 from ..constructor import construct_domain
 
-from .exceptions import (NonSquareMatrixError, ShapeError, DDMShapeError,
-        DDMDomainError, DDMFormatError)
+from .exceptions import NonSquareMatrixError, ShapeError
 
 from .ddm import DDM
 
@@ -65,13 +64,12 @@ class DomainMatrix:
     ========
 
     DDM
-    SDM
     Domain
     Poly
 
     """
 
-    def __new__(cls, rows, shape, domain, *, fmt=None):
+    def __init__(self, rows, shape, domain):
         """
         Creates a :py:class:`~.DomainMatrix`.
 
@@ -89,83 +87,16 @@ def __new__(cls, rows, shape, domain, *, fmt=None):
             If any of rows, shape and domain are not provided
 
         """
-        if isinstance(rows, (DDM, SDM)):
-            raise TypeError("Use from_rep to initialise from SDM/DDM")
-        elif isinstance(rows, list):
-            rep = DDM(rows, shape, domain)
-        elif isinstance(rows, dict):
-            rep = SDM(rows, shape, domain)
+        if isinstance(rows, list):
+            self.rep = SDM.from_list(rows, shape, domain)
         else:
-            msg = "Input should be list-of-lists or dict-of-dicts"
-            raise TypeError(msg)
-
-        if fmt is not None:
-            if fmt == 'sparse':
-                rep = rep.to_sdm()
-            elif fmt == 'dense':
-                rep = rep.to_ddm()
-            else:
-                raise ValueError("fmt should be 'sparse' or 'dense'")
-
-        return cls.from_rep(rep)
+            self.rep = SDM(rows, shape, domain)
+        self.shape = shape
+        self.domain = domain
 
     @classmethod
-    def from_rep(cls, rep):
-        """Create a new DomainMatrix efficiently from DDM/SDM.
-
-        Examples
-        ========
-
-        Create a :py:class:`~.DomainMatrix` with an dense internal
-        representation as :py:class:`~.DDM`:
-
-        >>> from sympy.polys.domains import ZZ
-        >>> from sympy.polys.matrices import DomainMatrix
-        >>> from sympy.polys.matrices.ddm import DDM
-        >>> drep = DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
-        >>> dM = DomainMatrix.from_rep(drep)
-        >>> dM
-        DomainMatrix([[1, 2], [3, 4]], (2, 2), ZZ)
-
-        Create a :py:class:`~.DomainMatrix` with a sparse internal
-        representation as :py:class:`~.SDM`:
-
-        >>> from sympy.polys.matrices import DomainMatrix
-        >>> from sympy.polys.matrices.sdm import SDM
-        >>> from sympy import ZZ
-        >>> drep = SDM({0:{1:ZZ(1)},1:{0:ZZ(2)}}, (2, 2), ZZ)
-        >>> dM = DomainMatrix.from_rep(drep)
-        >>> dM
-        DomainMatrix({0: {1: 1}, 1: {0: 2}}, (2, 2), ZZ)
-
-        Parameters
-        ==========
-
-        rep: SDM or DDM
-            The internal sparse or dense representation of the matrix.
-
-        Returns
-        =======
-
-        DomainMatrix
-            A :py:class:`~.DomainMatrix` wrapping *rep*.
-
-        Notes
-        =====
-
-        This takes ownership of rep as its internal representation. If rep is
-        being mutated elsewhere then a copy should be provided to
-        ``from_rep``. Only minimal verification or checking is done on *rep*
-        as this is supposed to be an efficient internal routine.
-
-        """
-        if not isinstance(rep, (DDM, SDM)):
-            raise TypeError("rep should be of type DDM or SDM")
-        self = super().__new__(cls)
-        self.rep = rep
-        self.shape = rep.shape
-        self.domain = rep.domain
-        return self
+    def from_rep(cls, ddm):
+        return cls(ddm, ddm.shape, ddm.domain)
 
     @classmethod
     def from_list_sympy(cls, nrows, ncols, rows, **kwargs):
@@ -305,135 +236,50 @@ def to_field(self):
         K = self.domain.get_field()
         return self.convert_to(K)
 
-    def to_sparse(self):
-        """
-        Return a sparse DomainMatrix representation of *self*.
-
-        Examples
-        ========
-
-        >>> from sympy.polys.matrices import DomainMatrix
-        >>> from sympy import QQ
-        >>> A = DomainMatrix([[1, 0],[0, 2]], (2, 2), QQ)
-        >>> A.rep
-        [[1, 0], [0, 2]]
-        >>> B = A.to_sparse()
-        >>> B.rep
-        {0: {0: 1}, 1: {1: 2}}
-        """
-        if self.rep.fmt == 'sparse':
-            return self
-
-        return self.from_rep(SDM.from_ddm(self.rep))
-
-    def to_dense(self):
-        """
-        Return a dense DomainMatrix representation of *self*.
-
-        Examples
-        ========
-
-        >>> from sympy.polys.matrices import DomainMatrix
-        >>> from sympy import QQ
-        >>> A = DomainMatrix({0: {0: 1}, 1: {1: 2}}, (2, 2), QQ)
-        >>> A.rep
-        {0: {0: 1}, 1: {1: 2}}
-        >>> B = A.to_dense()
-        >>> B.rep
-        [[1, 0], [0, 2]]
-
-        """
-        if self.rep.fmt == 'dense':
-            return self
-
-        return self.from_rep(SDM.to_ddm(self.rep))
-
-    def _unify_domain(self, other):
-        """Convert self and other to a common domain"""
-        K1 = self.domain
-        K2 = other.domain
-        if K1 == K2:
-            return self, other
-        K = K1.unify(K2)
-        if K1 != K:
-            self = self.convert_to(K)
-        if K2 != K:
-            other = other.convert_to(K)
-        return self, other
-
-    def _unify_fmt(self, other, fmt):
-        """Convert self and other to the same format.
-
-        If both are sparse or both are dense then return both unmodified.
-        Otherwise convert both to the preferred format given as *fmt* which
-        should be 'dense' or 'sparse'.
-        """
-        if self.rep.fmt == other.rep.fmt:
-            return self, other
-        elif fmt == 'sparse':
-            return self.to_sparse(), other.to_sparse()
-        elif fmt == 'dense':
-            return self.to_dense(), other.to_dense()
-        else:
-            raise ValueError("fmt should be 'sparse' or 'dense'")
-
-    def unify(self, other, *, fmt=None):
-        """
-        Unifies the domains and the format of self and other
-        matrices.
+    def unify(self, other):
+        r"""
+        Unify the domains of self and other
 
         Parameters
         ==========
 
         other : another DomainMatrix
-        fmt: string 'dense', 'sparse' or `None` (default)
-            The preferred format to convert to if self and other are not
-            already in the same format. If `None` or not specified then no
-            conversion if performed.
 
         Returns
         =======
 
         (dM1, dM2)
-            dM1, dM2 DomainMatrix matrices with unified Domain and format
+            dM1, dM2 DomainMatrix matrices with unified Domain
 
         Examples
         ========
 
-        Unify the domain of DomainMatrix that have different domains:
-
         >>> from sympy import ZZ, QQ
         >>> from sympy.polys.matrices import DomainMatrix
-        >>> A = DomainMatrix([[ZZ(1), ZZ(2)]], (1, 2), ZZ)
-        >>> B = DomainMatrix([[QQ(1, 2), QQ(2)]], (1, 2), QQ)
-        >>> Aq, Bq = A.unify(B)
-        >>> Aq
-        DomainMatrix([[1, 2]], (1, 2), QQ)
-        >>> Bq
-        DomainMatrix([[1/2, 2]], (1, 2), QQ)
-
-        Unify the format (dense or sparse):
-
-        >>> A = DomainMatrix([[ZZ(1), ZZ(2)]], (1, 2), ZZ)
-        >>> B = DomainMatrix({0:{0: ZZ(1)}}, (2, 2), ZZ)
-        >>> B.rep
-        {0: {0: 1}}
+        >>> A = DomainMatrix([
+        ...    [ZZ(1), ZZ(2), ZZ(3)]], (1, 3), ZZ)
+        >>> B = DomainMatrix([
+        ...    [QQ(1, 2), QQ(3, 5)]], (1, 2), QQ)
 
-        >>> A2, B2 = A.unify(B, fmt='dense')
-        >>> B2.rep
-        [[1, 0], [0, 0]]
+        >>> A.unify(B)
+        (DomainMatrix([[1, 2, 3]], (1, 3), QQ), DomainMatrix([[1/2, 3/5]], (1, 2), QQ))
 
         See Also
         ========
 
-        convert_to, to_dense, to_sparse
+        convert_to
 
         """
-
-        dM1, dM2 = self._unify_domain(other)
-        if fmt is not None:
-            dM1, dM2 = dM1._unify_fmt(dM2, fmt)
-        return dM1, dM2
+        K1 = self.domain
+        K2 = other.domain
+        if K1 == K2:
+            return self, other
+        K = K1.unify(K2)
+        if K1 != K:
+            self = self.convert_to(K)
+        if K2 != K:
+            other = other.convert_to(K)
+        return self, other
 
     def to_Matrix(self):
         r"""
@@ -471,7 +317,10 @@ def to_Matrix(self):
         return MutableDenseMatrix(rows_sympy)
 
     def __repr__(self):
-        return 'DomainMatrix(%s, %r, %r)' % (str(self.rep), self.shape, self.domain)
+        elemlist = self.rep.to_list()
+        rows_str = ['[%s]' % (', '.join(map(str, row))) for row in elemlist]
+        rowstr = '[%s]' % ', '.join(rows_str)
+        return 'DomainMatrix(%s, %r, %r)' % (rowstr, self.shape, self.domain)
 
     def hstack(A, B):
         r"""
@@ -494,8 +343,11 @@ def hstack(A, B):
 
         >>> from sympy import ZZ, QQ
         >>> from sympy.polys.matrices import DomainMatrix
-        >>> A = DomainMatrix([[ZZ(1), ZZ(2), ZZ(3)]], (1, 3), ZZ)
-        >>> B = DomainMatrix([[QQ(-1, 2), QQ(1, 2), QQ(1, 3)]],(1, 3), QQ)
+        >>> A = DomainMatrix([
+        ...    [ZZ(1), ZZ(2), ZZ(3)]], (1, 3), ZZ)
+        >>> B = DomainMatrix([
+        ...    [QQ(-1, 2), QQ(1, 2), QQ(1, 3)]],(1, 3), QQ)
+
         >>> A.hstack(B)
         DomainMatrix([[1, 2, 3, -1/2, 1/2, 1/3]], (1, 6), QQ)
 
@@ -505,19 +357,17 @@ def hstack(A, B):
         unify
 
         """
-        A, B = A.unify(B, fmt='dense')
+        A, B = A.unify(B)
         return A.from_rep(A.rep.hstack(B.rep))
 
     def __add__(A, B):
         if not isinstance(B, DomainMatrix):
             return NotImplemented
-        A, B = A.unify(B, fmt='dense')
         return A.add(B)
 
     def __sub__(A, B):
         if not isinstance(B, DomainMatrix):
             return NotImplemented
-        A, B = A.unify(B, fmt='dense')
         return A.sub(B)
 
     def __neg__(A):
@@ -526,7 +376,6 @@ def __neg__(A):
     def __mul__(A, B):
         """A * B"""
         if isinstance(B, DomainMatrix):
-            A, B = A.unify(B, fmt='dense')
             return A.matmul(B)
         elif B in A.domain:
             return A.from_rep(A.rep * B)
@@ -545,17 +394,6 @@ def __pow__(A, n):
             return NotImplemented
         return A.pow(n)
 
-    def _check(a, op, b, ashape, bshape):
-        if a.domain != b.domain:
-            msg = "Domain mismatch: %s %s %s" % (a.domain, op, b.domain)
-            raise DDMDomainError(msg)
-        if ashape != bshape:
-            msg = "Shape mismatch: %s %s %s" % (a.shape, op, b.shape)
-            raise DDMShapeError(msg)
-        if a.rep.fmt != b.rep.fmt:
-            msg = "Format mismatch: %s %s %s" % (a.rep.fmt, op, b.rep.fmt)
-            raise DDMFormatError(msg)
-
     def add(A, B):
         r"""
         Adds two DomainMatrix matrices of the same Domain
@@ -602,10 +440,12 @@ def add(A, B):
         sub, matmul
 
         """
-        A._check('+', B, A.shape, B.shape)
+        if A.shape != B.shape:
+            raise ShapeError("shape")
+        if A.domain != B.domain:
+            raise ValueError("domain")
         return A.from_rep(A.rep.add(B.rep))
 
-
     def sub(A, B):
         r"""
         Subtracts two DomainMatrix matrices of the same Domain
@@ -652,7 +492,10 @@ def sub(A, B):
         add, matmul
 
         """
-        A._check('-', B, A.shape, B.shape)
+        if A.shape != B.shape:
+            raise ShapeError("shape")
+        if A.domain != B.domain:
+            raise ValueError("domain")
         return A.from_rep(A.rep.sub(B.rep))
 
     def neg(A):
@@ -766,8 +609,6 @@ def matmul(A, B):
         mul, pow, add, sub
 
         """
-
-        A._check('*', B, A.shape[1], B.shape[0])
         return A.from_rep(A.rep.matmul(B.rep))
 
     def pow(A, n):
@@ -811,13 +652,14 @@ def pow(A, n):
         matmul
 
         """
-        nrows, ncols = A.shape
-        if nrows != ncols:
-            raise NonSquareMatrixError('Power of a nonsquare matrix')
         if n < 0:
             raise NotImplementedError('Negative powers')
         elif n == 0:
-            return A.eye(nrows, A.domain)
+            m, n = A.shape
+            rows = [[A.domain.zero] * m for _ in range(m)]
+            for i in range(m):
+                rows[i][i] = A.domain.one
+            return type(A)(rows, A.shape, A.domain)
         elif n == 1:
             return A
         elif n % 2 == 1:
@@ -1110,13 +952,13 @@ def eye(cls, n, domain):
         >>> from sympy.polys.matrices import DomainMatrix
         >>> from sympy import QQ
         >>> DomainMatrix.eye(3, QQ)
-        DomainMatrix({0: {0: 1}, 1: {1: 1}, 2: {2: 1}}, (3, 3), QQ)
+        DomainMatrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]], (3, 3), QQ)
 
         """
-        return cls.from_rep(SDM.eye(n, domain))
+        return cls.from_rep(DDM.eye(n, domain))
 
     @classmethod
-    def zeros(cls, shape, domain, *, fmt='sparse'):
+    def zeros(cls, shape, domain):
         """Returns a zero DomainMatrix of size shape, belonging to the specified domain
 
         Examples
@@ -1125,14 +967,15 @@ def zeros(cls, shape, domain, *, fmt='sparse'):
         >>> from sympy.polys.matrices import DomainMatrix
         >>> from sympy import QQ
         >>> DomainMatrix.zeros((2, 3), QQ)
-        DomainMatrix({}, (2, 3), QQ)
+        DomainMatrix([[0, 0, 0], [0, 0, 0]], (2, 3), QQ)
 
         """
-        return cls.from_rep(SDM.zeros(shape, domain))
+
+        return cls.from_rep(DDM.zeros(shape, domain))
 
     def __eq__(A, B):
         r"""
-        Checks for two DomainMatrix matrices to be equal or not
+        Checks for two DomainMatrix matrices two be equal or not
 
         Parameters
         ==========
diff --git a/sympy/polys/matrices/exceptions.py b/sympy/polys/matrices/exceptions.py
index 004e6b8b08..ce22a3b50b 100644
--- a/sympy/polys/matrices/exceptions.py
+++ b/sympy/polys/matrices/exceptions.py
@@ -33,13 +33,8 @@ class DDMShapeError(DDMError):
     pass
 
 
-class DDMFormatError(DDMError):
-    """mixed dense/sparse not supported"""
-    pass
-
-
 __all__ = [
-    'DDMError', 'DDMShapeError', 'DDMDomainError', 'DDMFormatError',
+    'DDMError', 'DDMShapeError', 'DDMDomainError',
 
     'NonSquareMatrixError', 'NonInvertibleMatrixError', 'ShapeError',
 ]
diff --git a/sympy/polys/matrices/sdm.py b/sympy/polys/matrices/sdm.py
index d8a7c09433..26d2e5744c 100644
--- a/sympy/polys/matrices/sdm.py
+++ b/sympy/polys/matrices/sdm.py
@@ -7,7 +7,7 @@
 from operator import add, neg, pos, sub
 from collections import defaultdict
 
-from .exceptions import DDMBadInputError, DDMDomainError, DDMShapeError
+from .exceptions import DDMBadInputError, DDMDomainError
 
 from .ddm import DDM
 
@@ -18,9 +18,6 @@ class SDM(dict):
     This is a dict subclass and is a wrapper for a dict of dicts that supports
     basic matrix arithmetic +, -, *, **.
     """
-
-    fmt = 'sparse'
-
     def __init__(self, elemsdict, shape, domain):
         super().__init__(elemsdict)
         self.shape = self.rows, self.cols = m, n = shape
@@ -31,18 +28,6 @@ def __init__(self, elemsdict, shape, domain):
         if not all(0 <= c < n for row in self.values() for c in row):
             raise DDMBadInputError("Column out of range")
 
-    def __str__(self):
-        rowsstr = []
-        for i, row in self.items():
-            elemsstr = ', '.join('%s: %s' % (j, elem) for j, elem in row.items())
-            rowsstr.append('%s: {%s}' % (i, elemsstr))
-        return '{%s}' % ', '.join(rowsstr)
-
-    def __repr__(self):
-        cls = type(self).__name__
-        rows = dict.__repr__(self)
-        return '%s(%s, %s, %s)' % (cls, rows, self.shape, self.domain)
-
     @classmethod
     def new(cls, sdm, shape, domain):
         return cls(sdm, shape, domain)
@@ -77,9 +62,6 @@ def to_list(M):
     def to_ddm(M):
         return DDM(M.to_list(), M.shape, M.domain)
 
-    def to_sdm(M):
-        return M
-
     @classmethod
     def zeros(cls, shape, domain):
         return cls({}, shape, domain)
@@ -91,7 +73,13 @@ def eye(cls, size, domain):
         return cls(sdm, (size, size), domain)
 
     def transpose(M):
-        MT = sdm_transpose(M)
+        MT = {}
+        for i, Mi in M.items():
+            for j, Mij in Mi.items():
+                try:
+                    MT[j][i] = Mij
+                except KeyError:
+                    MT[j] = {i: Mij}
         return M.new(MT, M.shape[::-1], M.domain)
 
     def __mul__(a, b):
@@ -109,12 +97,23 @@ def __rmul__(a, b):
     def matmul(A, B):
         if A.domain != B.domain:
             raise DDMDomainError
-        m, n = A.shape
-        n2, o = B.shape
-        if n != n2:
-            raise DDMShapeError
-        C = sdm_matmul(A, B)
-        return A.new(C, (m, o), A.domain)
+        zero = A.domain.zero
+        C = {}
+        BT = B.transpose()
+        for i, Ai in A.items():
+            Ai_ks = set(Ai)
+            Ci = {}
+            for j, BTj in BT.items():
+                BTj_ks = set(BTj)
+                knonzero = Ai_ks & BTj_ks
+                if knonzero:
+                    terms = (Ai[k] * BTj[k] for k in knonzero)
+                    Cij = sum(terms, zero)
+                    if Cij:
+                        Ci[j] = Cij
+            if Ci:
+                C[i] = Ci
+        return A.new(C, A.shape, A.domain)
 
     def mul(A, b):
         Csdm = unop_dict(A, lambda aij: aij*b)
@@ -235,58 +234,6 @@ def unop_dict(A, f):
     return B
 
 
-def sdm_transpose(M):
-    MT = {}
-    for i, Mi in M.items():
-        for j, Mij in Mi.items():
-            try:
-                MT[j][i] = Mij
-            except KeyError:
-                MT[j] = {i: Mij}
-    return MT
-
-
-def sdm_matmul(A, B):
-    #
-    # Should be fast if A and B are very sparse.
-    # Consider e.g. A = B = eye(1000).
-    #
-    # The idea here is that we compute C = A*B in terms of the rows of C and
-    # B since the dict of dicts representation naturally stores the matrix as
-    # rows. The ith row of C (Ci) is equal to the sum of Aik * Bk where Bk is
-    # the kth row of B. The algorithm below loops over each nonzero element
-    # Aik of A and if the corresponding row Bj is nonzero then we do
-    #    Ci += Aik * Bk.
-    # To make this more efficient we don't need to loop over all elements Aik.
-    # Instead for each row Ai we compute the intersection of the nonzero
-    # columns in Ai with the nonzero rows in B. That gives the k such that
-    # Aik and Bk are both nonzero. In Python the intersection of two sets
-    # of int can be computed very efficiently.
-    #
-    C = {}
-    B_knz = set(B)
-    for i, Ai in A.items():
-        Ci = {}
-        Ai_knz = set(Ai)
-        for k in Ai_knz & B_knz:
-            Aik = Ai[k]
-            for j, Bkj in B[k].items():
-                Cij = Ci.get(j, None)
-                if Cij is not None:
-                    Cij = Cij + Aik * Bkj
-                    if Cij:
-                        Ci[j] = Cij
-                    else:
-                        Ci.pop(j)
-                else:
-                    Cij = Aik * Bkj
-                    if Cij:
-                        Ci[j] = Cij
-        if Ci:
-            C[i] = Ci
-    return C
-
-
 def sdm_irref(A):
     """RREF and pivots of a sparse matrix *A*.
 
diff --git a/sympy/printing/latex.py b/sympy/printing/latex.py
index eb663eec7f..0c8ca73354 100644
--- a/sympy/printing/latex.py
+++ b/sympy/printing/latex.py
@@ -1968,12 +1968,10 @@ def _print_DiracDelta(self, expr, exp=None):
             tex = r"\left(%s\right)^{%s}" % (tex, exp)
         return tex
 
-    def _print_SingularityFunction(self, expr, exp=None):
+    def _print_SingularityFunction(self, expr):
         shift = self._print(expr.args[0] - expr.args[1])
         power = self._print(expr.args[2])
         tex = r"{\left\langle %s \right\rangle}^{%s}" % (shift, power)
-        if exp is not None:
-            tex = r"{\left({\langle %s \rangle}^{%s}\right)}^{%s}" % (shift, power, exp)
         return tex
 
     def _print_Heaviside(self, expr, exp=None):
diff --git a/sympy/sets/sets.py b/sympy/sets/sets.py
index 82704046fc..5275591e78 100644
--- a/sympy/sets/sets.py
+++ b/sympy/sets/sets.py
@@ -1284,15 +1284,14 @@ def is_subset(self, other):
 
     def as_relational(self, symbol):
         """Rewrite a Union in terms of equalities and logic operators. """
-        if (len(self.args) == 2 and
-                all(isinstance(i, Interval) for i in self.args)):
-            # optimization to give 3 args as (x > 1) & (x < 5) & Ne(x, 3)
-            # instead of as 4, ((1 <= x) & (x < 3)) | ((x <= 5) & (3 < x))
-            a, b = self.args
-            if (a.sup == b.inf and
-                    not any(a.sup in i for i in self.args)):
-                return And(Ne(symbol, a.sup), symbol < b.sup, symbol > a.inf)
-        return Or(*[i.as_relational(symbol) for i in self.args])
+        if all(isinstance(i, (FiniteSet, Interval)) for i in self.args):
+            if len(self.args) == 2:
+                a, b = self.args
+                if (a.sup == b.inf and a.inf is S.NegativeInfinity
+                        and b.sup is S.Infinity):
+                    return And(Ne(symbol, a.sup), symbol < b.sup, symbol > a.inf)
+            return Or(*[set.as_relational(symbol) for set in self.args])
+        raise NotImplementedError('relational of Union with non-Intervals')
 
     @property
     def is_iterable(self):
diff --git a/sympy/solvers/inequalities.py b/sympy/solvers/inequalities.py
index f6572017a5..f22dbeb94d 100644
--- a/sympy/solvers/inequalities.py
+++ b/sympy/solvers/inequalities.py
@@ -456,20 +456,6 @@ def solve_univariate_inequality(expr, gen, relational=True, domain=S.Reals, cont
     from sympy.solvers.solvers import denoms
     from sympy.solvers.solveset import solvify, solveset
 
-    if domain.is_subset(S.Reals) is False:
-        raise NotImplementedError(filldedent('''
-        Inequalities in the complex domain are
-        not supported. Try the real domain by
-        setting domain=S.Reals'''))
-    elif domain is not S.Reals:
-        rv = solve_univariate_inequality(
-        expr, gen, relational=False, continuous=continuous).intersection(domain)
-        if relational:
-            rv = rv.as_relational(gen)
-        return rv
-    else:
-        pass  # continue with attempt to solve in Real domain
-
     # This keeps the function independent of the assumptions about `gen`.
     # `solveset` makes sure this function is called only when the domain is
     # real.
diff --git a/sympy/solvers/solveset.py b/sympy/solvers/solveset.py
index aecdb2c2cb..d8ea49cdd4 100644
--- a/sympy/solvers/solveset.py
+++ b/sympy/solvers/solveset.py
@@ -1056,6 +1056,11 @@ def _solveset(f, symbol, domain, _check=False):
         result = solver(Add(f.lhs, - f.rhs, evaluate=False), symbol, domain)
 
     elif f.is_Relational:
+        if not domain.is_subset(S.Reals):
+            raise NotImplementedError(filldedent('''
+                Inequalities in the complex domain are
+                not supported. Try the real domain by
+                setting domain=S.Reals'''))
         try:
             result = solve_univariate_inequality(
             f, symbol, domain=domain, relational=False)
@@ -3014,52 +3019,52 @@ def add_intersection_complement(result, intersection_dict, complement_dict):
     # end of def add_intersection_complement()
 
     def _extract_main_soln(sym, sol, soln_imageset):
-        """Separate the Complements, Intersections, ImageSet lambda expr
-        and its base_set.
-        """
-        # if there is union, then need to check
-        # Complement, Intersection, Imageset.
-        # Order should not be changed.
-        if isinstance(sol, Complement):
-            # extract solution and complement
-            complements[sym] = sol.args[1]
-            sol = sol.args[0]
-            # complement will be added at the end
-            # using `add_intersection_complement` method
-        if isinstance(sol, Intersection):
-            # Interval/Set will be at 0th index always
-            if sol.args[0] not in (S.Reals, S.Complexes):
-                # Sometimes solveset returns soln with intersection
-                # S.Reals or S.Complexes. We don't consider that
-                # intersection.
-                intersections[sym] = sol.args[0]
-            sol = sol.args[1]
-        # after intersection and complement Imageset should
-        # be checked.
-        if isinstance(sol, ImageSet):
-            soln_imagest = sol
-            expr2 = sol.lamda.expr
-            sol = FiniteSet(expr2)
-            soln_imageset[expr2] = soln_imagest
-
-        # if there is union of Imageset or other in soln.
-        # no testcase is written for this if block
-        if isinstance(sol, Union):
-            sol_args = sol.args
-            sol = S.EmptySet
-            # We need in sequence so append finteset elements
-            # and then imageset or other.
-            for sol_arg2 in sol_args:
-                if isinstance(sol_arg2, FiniteSet):
-                    sol += sol_arg2
-                else:
-                    # ImageSet, Intersection, complement then
-                    # append them directly
-                    sol += FiniteSet(sol_arg2)
+            """Separate the Complements, Intersections, ImageSet lambda expr
+            and its base_set.
+            """
+            # if there is union, then need to check
+            # Complement, Intersection, Imageset.
+            # Order should not be changed.
+            if isinstance(sol, Complement):
+                # extract solution and complement
+                complements[sym] = sol.args[1]
+                sol = sol.args[0]
+                # complement will be added at the end
+                # using `add_intersection_complement` method
+            if isinstance(sol, Intersection):
+                # Interval/Set will be at 0th index always
+                if sol.args[0] not in (S.Reals, S.Complexes):
+                    # Sometimes solveset returns soln with intersection
+                    # S.Reals or S.Complexes. We don't consider that
+                    # intersection.
+                    intersections[sym] = sol.args[0]
+                sol = sol.args[1]
+            # after intersection and complement Imageset should
+            # be checked.
+            if isinstance(sol, ImageSet):
+                soln_imagest = sol
+                expr2 = sol.lamda.expr
+                sol = FiniteSet(expr2)
+                soln_imageset[expr2] = soln_imagest
+
+            # if there is union of Imageset or other in soln.
+            # no testcase is written for this if block
+            if isinstance(sol, Union):
+                sol_args = sol.args
+                sol = S.EmptySet
+                # We need in sequence so append finteset elements
+                # and then imageset or other.
+                for sol_arg2 in sol_args:
+                    if isinstance(sol_arg2, FiniteSet):
+                        sol += sol_arg2
+                    else:
+                        # ImageSet, Intersection, complement then
+                        # append them directly
+                        sol += FiniteSet(sol_arg2)
 
-        if not isinstance(sol, FiniteSet):
-            sol = FiniteSet(sol)
-        return sol, soln_imageset
+            if not isinstance(sol, FiniteSet):
+                sol = FiniteSet(sol)
+            return sol, soln_imageset
     # end of def _extract_main_soln()
 
     # helper function for _append_new_soln
@@ -3198,15 +3203,14 @@ def _solve_using_known_values(result, solver):
             result = _new_order_result(result, eq)
             for res in result:
                 got_symbol = set()  # symbols solved in one iteration
-                if soln_imageset:
-                    # find the imageset and use its expr.
-                    for key_res, value_res in res.items():
-                        if isinstance(value_res, ImageSet):
-                            res[key_res] = value_res.lamda.expr
-                            original_imageset[key_res] = value_res
-                            dummy_n = value_res.lamda.expr.atoms(Dummy).pop()
-                            (base,) = value_res.base_sets
-                            imgset_yes = (dummy_n, base)
+                # find the imageset and use its expr.
+                for key_res, value_res in res.items():
+                    if isinstance(value_res, ImageSet):
+                        res[key_res] = value_res.lamda.expr
+                        original_imageset[key_res] = value_res
+                        dummy_n = value_res.lamda.expr.atoms(Dummy).pop()
+                        (base,) = value_res.base_sets
+                        imgset_yes = (dummy_n, base)
                 # update eq with everything that is known so far
                 eq2 = eq.subs(res).expand()
                 unsolved_syms = _unsolved_syms(eq2, sort=True)


Test patch:
diff --git a/sympy/geometry/tests/test_ellipse.py b/sympy/geometry/tests/test_ellipse.py
index 6d0c70bce7..8a28bc0270 100644
--- a/sympy/geometry/tests/test_ellipse.py
+++ b/sympy/geometry/tests/test_ellipse.py
@@ -157,12 +157,6 @@ def test_ellipse_geom():
     assert Circle(Point(5, 5), 2).tangent_lines(Point(5 - 2*sqrt(2), 5)) == \
         [Line(Point(5 - 2*sqrt(2), 5), Point(5 - sqrt(2), 5 - sqrt(2))),
      Line(Point(5 - 2*sqrt(2), 5), Point(5 - sqrt(2), 5 + sqrt(2))), ]
-    assert Circle(Point(5, 5), 5).tangent_lines(Point(4, 0)) == \
-        [Line(Point(4, 0), Point(Rational(40, 13), Rational(5, 13))),
-     Line(Point(4, 0), Point(5, 0))]
-    assert Circle(Point(5, 5), 5).tangent_lines(Point(0, 6)) == \
-        [Line(Point(0, 6), Point(0, 7)),
-        Line(Point(0, 6), Point(Rational(5, 13), Rational(90, 13)))]
 
     # for numerical calculations, we shouldn't demand exact equality,
     # so only test up to the desired precision
diff --git a/sympy/integrals/tests/test_meijerint.py b/sympy/integrals/tests/test_meijerint.py
index c333a40292..c4cc4df239 100644
--- a/sympy/integrals/tests/test_meijerint.py
+++ b/sympy/integrals/tests/test_meijerint.py
@@ -625,11 +625,11 @@ def test_messy():
                        fourier_transform, sqrt)
     assert laplace_transform(Si(x), x, s) == ((-atan(s) + pi/2)/s, 0, True)
 
-    assert laplace_transform(Shi(x), x, s) == (acoth(s)/s, 1, s > 1)
+    assert laplace_transform(Shi(x), x, s) == (acoth(s)/s, 1, True)
 
     # where should the logs be simplified?
     assert laplace_transform(Chi(x), x, s) == \
-        ((log(s**(-2)) - log(1 - 1/s**2))/(2*s), 1, s > 1)
+        ((log(s**(-2)) - log(1 - 1/s**2))/(2*s), 1, True)
 
     # TODO maybe simplify the inequalities?
     assert laplace_transform(besselj(a, x), x, s)[1:] == \
diff --git a/sympy/integrals/tests/test_transforms.py b/sympy/integrals/tests/test_transforms.py
index d4609719d6..4c3e79984f 100644
--- a/sympy/integrals/tests/test_transforms.py
+++ b/sympy/integrals/tests/test_transforms.py
@@ -518,20 +518,20 @@ def test_laplace_transform():
 
     assert LT(Matrix([[exp(t), t*exp(-t)], [t*exp(-t), exp(t)]]), t, s) ==\
         Matrix([
-            [(1/(s - 1), 1, s > 1), ((s + 1)**(-2), 0, True)],
-            [((s + 1)**(-2), 0, True), (1/(s - 1), 1, s > 1)]
+            [(1/(s - 1), 1, True), ((s + 1)**(-2), 0, True)],
+            [((s + 1)**(-2), 0, True), (1/(s - 1), 1, True)]
         ])
 
 
 def test_issue_8368_7173():
     LT = laplace_transform
     # hyperbolic
-    assert LT(sinh(x), x, s) == (1/(s**2 - 1), 1, s > 1)
-    assert LT(cosh(x), x, s) == (s/(s**2 - 1), 1, s > 1)
+    assert LT(sinh(x), x, s) == (1/(s**2 - 1), 1, True)
+    assert LT(cosh(x), x, s) == (s/(s**2 - 1), 1, True)
     assert LT(sinh(x + 3), x, s) == (
-        (-s + (s + 1)*exp(6) + 1)*exp(-3)/(s - 1)/(s + 1)/2, 1, s > 1)
+        (-s + (s + 1)*exp(6) + 1)*exp(-3)/(s - 1)/(s + 1)/2, 1, True)
     assert LT(sinh(x)*cosh(x), x, s) == (
-        1/(s**2 - 4), 2, s > 2)
+        1/(s**2 - 4), 2, Ne(s/2, 1))
     # trig (make sure they are not being rewritten in terms of exp)
     assert LT(cos(x + 3), x, s) == ((s*cos(3) - sin(3))/(s**2 + 1), 0, True)
 
diff --git a/sympy/matrices/expressions/tests/test_matexpr.py b/sympy/matrices/expressions/tests/test_matexpr.py
index c88d60560f..83499fd982 100644
--- a/sympy/matrices/expressions/tests/test_matexpr.py
+++ b/sympy/matrices/expressions/tests/test_matexpr.py
@@ -1,9 +1,8 @@
 from sympy import (KroneckerDelta, diff, Sum, Dummy, factor,
                    expand, zeros, gcd_terms, Eq, Symbol)
 
-from sympy.core import (S, symbols, Add, Mul, SympifyError, Rational,
-                    Function)
-from sympy.functions import sin, cos, tan, sqrt, cbrt, exp
+from sympy.core import S, symbols, Add, Mul, SympifyError, Rational
+from sympy.functions import sin, cos, sqrt, cbrt, exp
 from sympy.simplify import simplify
 from sympy.matrices import (ImmutableMatrix, Inverse, MatAdd, MatMul,
         MatPow, Matrix, MatrixExpr, MatrixSymbol, ShapeError,
@@ -341,18 +340,6 @@ def test_issue_7842():
     assert Eq(A, B) == True
 
 
-def test_issue_21195():
-    t = symbols('t')
-    x = Function('x')(t)
-    dx = x.diff(t)
-    exp1 = cos(x) + cos(x)*dx
-    exp2 = sin(x) + tan(x)*(dx.diff(t))
-    exp3 = sin(x)*sin(t)*(dx.diff(t)).diff(t)
-    A = Matrix([[exp1], [exp2], [exp3]])
-    B = Matrix([[exp1.diff(x)], [exp2.diff(x)], [exp3.diff(x)]])
-    assert A.diff(x) == B
-
-
 def test_MatMul_postprocessor():
     z = zeros(2)
     z1 = ZeroMatrix(2, 2)
diff --git a/sympy/polys/matrices/tests/test_ddm.py b/sympy/polys/matrices/tests/test_ddm.py
index 447c6f3fc6..0642d1ce1b 100644
--- a/sympy/polys/matrices/tests/test_ddm.py
+++ b/sympy/polys/matrices/tests/test_ddm.py
@@ -40,11 +40,9 @@ def test_DDM_getsetitem():
 def test_DDM_str():
     ddm = DDM([[ZZ(0), ZZ(1)], [ZZ(2), ZZ(3)]], (2, 2), ZZ)
     if HAS_GMPY: # pragma: no cover
-        assert str(ddm) == '[[0, 1], [2, 3]]'
-        assert repr(ddm) == 'DDM([[mpz(0), mpz(1)], [mpz(2), mpz(3)]], (2, 2), ZZ)'
+        assert str(ddm) == 'DDM([[mpz(0), mpz(1)], [mpz(2), mpz(3)]], (2, 2), ZZ)'
     else:        # pragma: no cover
-        assert repr(ddm) == 'DDM([[0, 1], [2, 3]], (2, 2), ZZ)'
-        assert str(ddm) == '[[0, 1], [2, 3]]'
+        assert str(ddm) == 'DDM([[0, 1], [2, 3]], (2, 2), ZZ)'
 
 
 def test_DDM_eq():
@@ -73,13 +71,6 @@ def test_DDM_eq():
     assert (ddm3 != ddm1) is True
 
 
-def test_DDM_convert_to():
-    ddm = DDM([[ZZ(1), ZZ(2)]], (1, 2), ZZ)
-    assert ddm.convert_to(ZZ) == ddm
-    ddmq = ddm.convert_to(QQ)
-    assert ddmq.domain == QQ
-
-
 def test_DDM_zeros():
     ddmz = DDM.zeros((3, 4), QQ)
     assert list(ddmz) == [[QQ(0)] * 4] * 3
@@ -197,15 +188,6 @@ def test_DDM_matmul():
     raises(DDMShapeError, lambda: Z05 @ Z40)
     raises(DDMShapeError, lambda: Z05.matmul(Z40))
 
-def test_DDM_hstack():
-
-    A = DDM([[ZZ(1), ZZ(2), ZZ(3)]], (1, 3), ZZ)
-    B = DDM([[ZZ(4), ZZ(5)]], (1, 2), ZZ)
-    Ah = A.hstack(B)
-
-    assert Ah.shape == (1, 5)
-    assert Ah.domain == ZZ
-    assert Ah == DDM([[ZZ(1), ZZ(2), ZZ(3), ZZ(4), ZZ(5)]], (1, 5), ZZ)
 
 def test_DDM_rref():
 
@@ -241,8 +223,7 @@ def test_DDM_rref():
 def test_DDM_nullspace():
      A = DDM([[QQ(1), QQ(1)], [QQ(1), QQ(1)]], (2, 2), QQ)
      Anull = DDM([[QQ(-1), QQ(1)]], (1, 2), QQ)
-     nonpivots = [1]
-     assert A.nullspace() == (Anull, nonpivots)
+     assert A.nullspace() == Anull
 
 
 def test_DDM_det():
diff --git a/sympy/polys/matrices/tests/test_domainmatrix.py b/sympy/polys/matrices/tests/test_domainmatrix.py
index 51e3290935..7657f9542e 100644
--- a/sympy/polys/matrices/tests/test_domainmatrix.py
+++ b/sympy/polys/matrices/tests/test_domainmatrix.py
@@ -9,62 +9,33 @@
 from sympy.polys import ZZ, QQ
 
 from sympy.polys.matrices.domainmatrix import DomainMatrix
-from sympy.polys.matrices.exceptions import (DDMBadInputError, DDMDomainError,
-        DDMShapeError, DDMFormatError)
+from sympy.polys.matrices.exceptions import DDMBadInputError, DDMDomainError
 from sympy.polys.matrices.ddm import DDM
 from sympy.polys.matrices.sdm import SDM
 
 
 def test_DomainMatrix_init():
-    lol = [[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]]
-    dod = {0: {0: ZZ(1), 1:ZZ(2)}, 1: {0:ZZ(3), 1:ZZ(4)}}
-    ddm = DDM(lol, (2, 2), ZZ)
-    sdm = SDM(dod, (2, 2), ZZ)
-
-    A = DomainMatrix(lol, (2, 2), ZZ)
-    assert A.rep == ddm
-    assert A.shape == (2, 2)
-    assert A.domain == ZZ
-
-    A = DomainMatrix(dod, (2, 2), ZZ)
-    assert A.rep == sdm
+    A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
+    # assert A.rep == DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
+    assert A.rep == SDM({0: {0: ZZ(1), 1:ZZ(2)}, 1: {0:ZZ(3), 1:ZZ(4)}}, (2, 2), ZZ)
     assert A.shape == (2, 2)
     assert A.domain == ZZ
 
-    raises(TypeError, lambda: DomainMatrix(ddm, (2, 2), ZZ))
-    raises(TypeError, lambda: DomainMatrix(sdm, (2, 2), ZZ))
-    raises(TypeError, lambda: DomainMatrix(Matrix([[1]]), (1, 1), ZZ))
-
-    for fmt, rep in [('sparse', sdm), ('dense', ddm)]:
-        A = DomainMatrix(lol, (2, 2), ZZ, fmt=fmt)
-        assert A.rep == rep
-        A = DomainMatrix(dod, (2, 2), ZZ, fmt=fmt)
-        assert A.rep == rep
-
-    raises(ValueError, lambda: DomainMatrix(lol, (2, 2), ZZ, fmt='invalid'))
-
     raises(DDMBadInputError, lambda: DomainMatrix([[ZZ(1), ZZ(2)]], (2, 2), ZZ))
 
 
 def test_DomainMatrix_from_rep():
-    ddm = DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
+    # ddm = DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
+    ddm = SDM({0: {0: ZZ(1), 1:ZZ(2)}, 1: {0:ZZ(3), 1:ZZ(4)}}, (2, 2), ZZ)
     A = DomainMatrix.from_rep(ddm)
     assert A.rep == ddm
     assert A.shape == (2, 2)
     assert A.domain == ZZ
 
-    sdm = SDM({0: {0: ZZ(1), 1:ZZ(2)}, 1: {0:ZZ(3), 1:ZZ(4)}}, (2, 2), ZZ)
-    A = DomainMatrix.from_rep(sdm)
-    assert A.rep == sdm
-    assert A.shape == (2, 2)
-    assert A.domain == ZZ
-
-    A = DomainMatrix([[ZZ(1)]], (1, 1), ZZ)
-    raises(TypeError, lambda: DomainMatrix.from_rep(A))
-
 
 def test_DomainMatrix_from_list_sympy():
-    ddm = DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
+    # ddm = DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
+    ddm = SDM({0: {0: ZZ(1), 1:ZZ(2)}, 1: {0:ZZ(3), 1:ZZ(4)}}, (2, 2), ZZ)
     A = DomainMatrix.from_list_sympy(2, 2, [[1, 2], [3, 4]])
     assert A.rep == ddm
     assert A.shape == (2, 2)
@@ -77,6 +48,7 @@ def test_DomainMatrix_from_list_sympy():
         (2, 2),
         K
     )
+    ddm = SDM.from_ddm(ddm)
     A = DomainMatrix.from_list_sympy(
         2, 2, [[1 + sqrt(2), 2 + sqrt(2)], [3 + sqrt(2), 4 + sqrt(2)]],
         extension=True)
@@ -87,6 +59,7 @@ def test_DomainMatrix_from_list_sympy():
 
 def test_DomainMatrix_from_Matrix():
     ddm = DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
+    ddm = SDM.from_ddm(ddm)
     A = DomainMatrix.from_Matrix(Matrix([[1, 2], [3, 4]]))
     assert A.rep == ddm
     assert A.shape == (2, 2)
@@ -99,6 +72,7 @@ def test_DomainMatrix_from_Matrix():
         (2, 2),
         K
     )
+    ddm = SDM.from_ddm(ddm)
     A = DomainMatrix.from_Matrix(
         Matrix([[1 + sqrt(2), 2 + sqrt(2)], [3 + sqrt(2), 4 + sqrt(2)]]),
         extension=True)
@@ -138,18 +112,6 @@ def test_DomainMatrix_to_field():
     assert Aq == DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
 
 
-def test_DomainMatrix_to_sparse():
-    A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
-    A_sparse = A.to_sparse()
-    assert A_sparse.rep == {0: {0: 1, 1: 2}, 1: {0: 3, 1: 4}}
-
-
-def test_DomainMatrix_to_dense():
-    A = DomainMatrix({0: {0: 1, 1: 2}, 1: {0: 3, 1: 4}}, (2, 2), ZZ)
-    A_dense = A.to_dense()
-    assert A_dense.rep == DDM([[1, 2], [3, 4]], (2, 2), ZZ)
-
-
 def test_DomainMatrix_unify():
     Az = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
     Aq = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
@@ -158,22 +120,6 @@ def test_DomainMatrix_unify():
     assert Aq.unify(Az) == (Aq, Aq)
     assert Aq.unify(Aq) == (Aq, Aq)
 
-    As = DomainMatrix({0: {1: ZZ(1)}, 1:{0:ZZ(2)}}, (2, 2), ZZ)
-    Ad = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
-
-    assert As.unify(As) == (As, As)
-    assert Ad.unify(Ad) == (Ad, Ad)
-
-    Bs, Bd = As.unify(Ad, fmt='dense')
-    assert Bs.rep == DDM([[0, 1], [2, 0]], (2, 2), ZZ)
-    assert Bd.rep == DDM([[1, 2],[3, 4]], (2, 2), ZZ)
-
-    Bs, Bd = As.unify(Ad, fmt='sparse')
-    assert Bs.rep == SDM({0: {1: 1}, 1: {0: 2}}, (2, 2), ZZ)
-    assert Bd.rep == SDM({0: {0: 1, 1: 2}, 1: {0: 3, 1: 4}}, (2, 2), ZZ)
-
-    raises(ValueError, lambda: As.unify(Ad, fmt='invalid'))
-
 
 def test_DomainMatrix_to_Matrix():
     A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
@@ -197,29 +143,17 @@ def test_DomainMatrix_add():
 
     A1 = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
     A2 = DomainMatrix([[ZZ(1), ZZ(2)]], (1, 2), ZZ)
-    raises(DDMShapeError, lambda: A1 + A2)
-    raises(DDMShapeError, lambda: A2 + A1)
-    raises(DDMShapeError, lambda: A1.add(A2))
-    raises(DDMShapeError, lambda: A2.add(A1))
+    raises(ShapeError, lambda: A1 + A2)
+    raises(ShapeError, lambda: A2 + A1)
+    raises(ShapeError, lambda: A1.add(A2))
+    raises(ShapeError, lambda: A2.add(A1))
 
     Az = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
     Aq = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
-    Asum = DomainMatrix([[QQ(2), QQ(4)], [QQ(6), QQ(8)]], (2, 2), QQ)
-    assert Az + Aq == Asum
-    assert Aq + Az == Asum
-    raises(DDMDomainError, lambda: Az.add(Aq))
-    raises(DDMDomainError, lambda: Aq.add(Az))
-
-    As = DomainMatrix({0: {1: ZZ(1)}, 1: {0: ZZ(2)}}, (2, 2), ZZ)
-    Ad = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
-
-    Asd = As + Ad
-    Ads = Ad + As
-    assert Asd == DomainMatrix([[1, 3], [5, 4]], (2, 2), ZZ)
-    assert Asd.rep == DDM([[1, 3], [5, 4]], (2, 2), ZZ)
-    assert Ads == DomainMatrix([[1, 3], [5, 4]], (2, 2), ZZ)
-    assert Ads.rep == DDM([[1, 3], [5, 4]], (2, 2), ZZ)
-    raises(DDMFormatError, lambda: As.add(Ad))
+    raises(ValueError, lambda: Az + Aq)
+    raises(ValueError, lambda: Aq + Az)
+    raises(ValueError, lambda: Az.add(Aq))
+    raises(ValueError, lambda: Aq.add(Az))
 
 
 def test_DomainMatrix_sub():
@@ -234,28 +168,17 @@ def test_DomainMatrix_sub():
 
     A1 = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
     A2 = DomainMatrix([[ZZ(1), ZZ(2)]], (1, 2), ZZ)
-    raises(DDMShapeError, lambda: A1 - A2)
-    raises(DDMShapeError, lambda: A2 - A1)
-    raises(DDMShapeError, lambda: A1.sub(A2))
-    raises(DDMShapeError, lambda: A2.sub(A1))
+    raises(ShapeError, lambda: A1 - A2)
+    raises(ShapeError, lambda: A2 - A1)
+    raises(ShapeError, lambda: A1.sub(A2))
+    raises(ShapeError, lambda: A2.sub(A1))
 
     Az = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
     Aq = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
-    Adiff = DomainMatrix([[QQ(0), QQ(0)], [QQ(0), QQ(0)]], (2, 2), QQ)
-    assert Az - Aq == Adiff
-    assert Aq - Az == Adiff
-    raises(DDMDomainError, lambda: Az.sub(Aq))
-    raises(DDMDomainError, lambda: Aq.sub(Az))
-
-    As = DomainMatrix({0: {1: ZZ(1)}, 1: {0: ZZ(2)}}, (2, 2), ZZ)
-    Ad = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
-
-    Asd = As - Ad
-    Ads = Ad - As
-    assert Asd == DomainMatrix([[-1, -1], [-1, -4]], (2, 2), ZZ)
-    assert Asd.rep == DDM([[-1, -1], [-1, -4]], (2, 2), ZZ)
-    assert Asd == -Ads
-    assert Asd.rep == -Ads.rep
+    raises(ValueError, lambda: Az - Aq)
+    raises(ValueError, lambda: Aq - Az)
+    raises(ValueError, lambda: Az.sub(Aq))
+    raises(ValueError, lambda: Aq.sub(Az))
 
 
 def test_DomainMatrix_neg():
@@ -276,9 +199,8 @@ def test_DomainMatrix_mul():
 
     Az = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
     Aq = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
-    Aprod = DomainMatrix([[QQ(7), QQ(10)], [QQ(15), QQ(22)]], (2, 2), QQ)
-    assert Az * Aq == Aprod
-    assert Aq * Az == Aprod
+    raises(DDMDomainError, lambda: Az * Aq)
+    raises(DDMDomainError, lambda: Aq * Az)
     raises(DDMDomainError, lambda: Az.matmul(Aq))
     raises(DDMDomainError, lambda: Aq.matmul(Az))
 
@@ -292,22 +214,12 @@ def test_DomainMatrix_mul():
     x = ZZ(0)
     assert A * x == x * A == A.mul(x) == AA
 
-    As = DomainMatrix({0: {1: ZZ(1)}, 1: {0: ZZ(2)}}, (2, 2), ZZ)
-    Ad = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
-
-    Asd = As * Ad
-    Ads = Ad * As
-    assert Asd == DomainMatrix([[3, 4], [2, 4]], (2, 2), ZZ)
-    assert Asd.rep == DDM([[3, 4], [2, 4]], (2, 2), ZZ)
-    assert Ads == DomainMatrix([[4, 1], [8, 3]], (2, 2), ZZ)
-    assert Ads.rep == DDM([[4, 1], [8, 3]], (2, 2), ZZ)
-
 
 def test_DomainMatrix_pow():
-    eye = DomainMatrix.eye(2, ZZ)
     A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
     A2 = DomainMatrix([[ZZ(7), ZZ(10)], [ZZ(15), ZZ(22)]], (2, 2), ZZ)
     A3 = DomainMatrix([[ZZ(37), ZZ(54)], [ZZ(81), ZZ(118)]], (2, 2), ZZ)
+    eye = DomainMatrix([[ZZ(1), ZZ(0)], [ZZ(0), ZZ(1)]], (2, 2), ZZ)
     assert A**0 == A.pow(0) == eye
     assert A**1 == A.pow(1) == A
     assert A**2 == A.pow(2) == A2
@@ -317,9 +229,6 @@ def test_DomainMatrix_pow():
     raises(NotImplementedError, lambda: A ** -1)
     raises(NotImplementedError, lambda: A.pow(-1))
 
-    A = DomainMatrix.zeros((2, 1), ZZ)
-    raises(NonSquareMatrixError, lambda: A ** 1)
-
 
 def test_DomainMatrix_rref():
     A = DomainMatrix([], (0, 1), QQ)
@@ -521,20 +430,13 @@ def test_DomainMatrix_charpoly():
 
 def test_DomainMatrix_eye():
     A = DomainMatrix.eye(3, QQ)
+    #assert A.rep == DDM.eye(3, QQ)
     assert A.rep == SDM.eye(3, QQ)
     assert A.shape == (3, 3)
     assert A.domain == QQ
 
-
 def test_DomainMatrix_zeros():
     A = DomainMatrix.zeros((1, 2), QQ)
     assert A.rep == SDM.zeros((1, 2), QQ)
     assert A.shape == (1, 2)
     assert A.domain == QQ
-
-
-def test_DomainMatrix_hstack():
-    A = DomainMatrix([[ZZ(1)], [ZZ(2)]], (2, 1), ZZ)
-    B = DomainMatrix([[QQ(3), QQ(4)], [QQ(5), QQ(6)]], (2, 2), QQ)
-    AB = DomainMatrix([[QQ(1), QQ(3), QQ(4)], [QQ(2), QQ(5), QQ(6)]], (2, 3), QQ)
-    assert A.hstack(B) == AB
diff --git a/sympy/polys/matrices/tests/test_sdm.py b/sympy/polys/matrices/tests/test_sdm.py
index cb5c2850e1..95259fa048 100644
--- a/sympy/polys/matrices/tests/test_sdm.py
+++ b/sympy/polys/matrices/tests/test_sdm.py
@@ -2,14 +2,13 @@
 Tests for the basic functionality of the SDM class.
 """
 
-from sympy.core.compatibility import HAS_GMPY
+
 from sympy.testing.pytest import raises
 
 from sympy import QQ, ZZ
 from sympy.polys.matrices.sdm import SDM
 from sympy.polys.matrices.ddm import DDM
-from sympy.polys.matrices.exceptions import (DDMBadInputError, DDMDomainError,
-        DDMShapeError)
+from sympy.polys.matrices.exceptions import DDMBadInputError, DDMDomainError
 
 
 def test_SDM():
@@ -22,15 +21,6 @@ def test_SDM():
     raises(DDMBadInputError, lambda: SDM({0:{5:ZZ(0)}}, (2, 2), ZZ))
 
 
-def test_DDM_str():
-    sdm = SDM({0:{0:ZZ(1)}, 1:{1:ZZ(1)}}, (2, 2), ZZ)
-    assert str(sdm) == '{0: {0: 1}, 1: {1: 1}}'
-    if HAS_GMPY: # pragma: no cover
-        assert repr(sdm) == 'SDM({0: {0: mpz(1)}, 1: {1: mpz(1)}}, (2, 2), ZZ)'
-    else:        # pragma: no cover
-        assert repr(sdm) == 'SDM({0: {0: 1}, 1: {1: 1}}, (2, 2), ZZ)'
-
-
 def test_SDM_new():
     A = SDM({0:{0:ZZ(1)}}, (2, 2), ZZ)
     B = A.new({}, (2, 2), ZZ)
@@ -128,19 +118,6 @@ def test_SDM_matmul():
     B = SDM({0:{0:ZZ(7), 1:ZZ(10)}, 1:{0:ZZ(15), 1:ZZ(22)}}, (2, 2), ZZ)
     assert A.matmul(A) == B
 
-    A22 = SDM({0:{0:ZZ(4)}}, (2, 2), ZZ)
-    A32 = SDM({0:{0:ZZ(2)}}, (3, 2), ZZ)
-    A23 = SDM({0:{0:ZZ(4)}}, (2, 3), ZZ)
-    A33 = SDM({0:{0:ZZ(8)}}, (3, 3), ZZ)
-    A22 = SDM({0:{0:ZZ(8)}}, (2, 2), ZZ)
-    assert A32.matmul(A23) == A33
-    assert A23.matmul(A32) == A22
-    # XXX: @ not supported by SDM...
-    #assert A32.matmul(A23) == A32 @ A23 == A33
-    #assert A23.matmul(A32) == A23 @ A32 == A22
-    #raises(DDMShapeError, lambda: A23 @ A22)
-    raises(DDMShapeError, lambda: A23.matmul(A22))
-
 
 def test_SDM_add():
     A = SDM({0:{1:ZZ(1)}, 1:{0:ZZ(2), 1:ZZ(3)}}, (2, 2), ZZ)
@@ -180,16 +157,6 @@ def test_SDM_convert_to():
     assert D.domain == ZZ
 
 
-def test_SDM_hstack():
-    A = SDM({0:{1:ZZ(1)}}, (2, 2), ZZ)
-    B = SDM({1:{1:ZZ(1)}}, (2, 2), ZZ)
-    AA = SDM({0:{1:ZZ(1), 3:ZZ(1)}}, (2, 4), ZZ)
-    AB = SDM({0:{1:ZZ(1)}, 1:{3:ZZ(1)}}, (2, 4), ZZ)
-    assert SDM.hstack(A) == A
-    assert SDM.hstack(A, A) == AA
-    assert SDM.hstack(A, B) == AB
-
-
 def test_SDM_inv():
     A = SDM({0:{0:QQ(1), 1:QQ(2)}, 1:{0:QQ(3), 1:QQ(4)}}, (2, 2), QQ)
     B = SDM({0:{0:QQ(-2), 1:QQ(1)}, 1:{0:QQ(3, 2), 1:QQ(-1, 2)}}, (2, 2), QQ)
diff --git a/sympy/printing/tests/test_latex.py b/sympy/printing/tests/test_latex.py
index f04d04c404..84227a1785 100644
--- a/sympy/printing/tests/test_latex.py
+++ b/sympy/printing/tests/test_latex.py
@@ -214,19 +214,6 @@ def test_latex_SingularityFunction():
     assert latex(SingularityFunction(x, 4, -1)) == \
         r"{\left\langle x - 4 \right\rangle}^{-1}"
 
-    assert latex(SingularityFunction(x, 4, 5)**3) == \
-        r"{\left({\langle x - 4 \rangle}^{5}\right)}^{3}"
-    assert latex(SingularityFunction(x, -3, 4)**3) == \
-        r"{\left({\langle x + 3 \rangle}^{4}\right)}^{3}"
-    assert latex(SingularityFunction(x, 0, 4)**3) == \
-        r"{\left({\langle x \rangle}^{4}\right)}^{3}"
-    assert latex(SingularityFunction(x, a, n)**3) == \
-        r"{\left({\langle - a + x \rangle}^{n}\right)}^{3}"
-    assert latex(SingularityFunction(x, 4, -2)**3) == \
-        r"{\left({\langle x - 4 \rangle}^{-2}\right)}^{3}"
-    assert latex((SingularityFunction(x, 4, -1)**3)**3) == \
-        r"{\left({\langle x - 4 \rangle}^{-1}\right)}^{9}"
-
 
 def test_latex_cycle():
     assert latex(Cycle(1, 2, 4)) == r"\left( 1\; 2\; 4\right)"
diff --git a/sympy/sets/tests/test_sets.py b/sympy/sets/tests/test_sets.py
index 6a6a00693f..0cf7c454f5 100644
--- a/sympy/sets/tests/test_sets.py
+++ b/sympy/sets/tests/test_sets.py
@@ -917,10 +917,6 @@ def test_Union_as_relational():
         Or(And(Le(0, x), Le(x, 1)), Eq(x, 2))
     assert (Interval(0, 1, True, True) + FiniteSet(1)).as_relational(x) == \
         And(Lt(0, x), Le(x, 1))
-    assert Or(x < 0, x > 0).as_set().as_relational(x) == \
-        And((x > -oo), (x < oo), Ne(x, 0))
-    assert (Interval.Ropen(1, 3) + Interval.Lopen(3, 5)
-        ).as_relational(x) == And((x > 1), (x < 5), Ne(x, 3))
 
 
 def test_Intersection_as_relational():
diff --git a/sympy/solvers/tests/test_inequalities.py b/sympy/solvers/tests/test_inequalities.py
index 726dc0172e..83a1cfd3c8 100644
--- a/sympy/solvers/tests/test_inequalities.py
+++ b/sympy/solvers/tests/test_inequalities.py
@@ -14,7 +14,6 @@
 from sympy.solvers.solvers import solve
 from sympy.solvers.solveset import solveset
 from sympy.abc import x, y
-from sympy.functions.elementary.integers import floor
 
 from sympy.testing.pytest import raises, XFAIL
 
@@ -297,7 +296,7 @@ def test_solve_univariate_inequality():
     assert isolve(1/(x - 2) > 0, x) == And(S(2) < x, x < oo)
     den = ((x - 1)*(x - 2)).expand()
     assert isolve((x - 1)/den <= 0, x) == \
-        (x > -oo) & (x < 2) & Ne(x, 1)
+        Or(And(-oo < x, x < 1), And(S.One < x, x < 2))
 
     n = Dummy('n')
     raises(NotImplementedError, lambda: isolve(Abs(x) <= n, x, relational=False))
@@ -377,8 +376,9 @@ def test_issue_8974():
 
 def test_issue_10198():
     assert reduce_inequalities(
-        -1 + 1/abs(1/x - 1) < 0) == (x > -oo) & (x < 1/2) & Ne(x, 0)
-
+        -1 + 1/abs(1/x - 1) < 0) == Or(
+        And(-oo < x, x < 0), And(S.Zero < x, x < S.Half)
+        )
     assert reduce_inequalities(abs(1/sqrt(x)) - 1, x) == Eq(x, 1)
     assert reduce_abs_inequality(-3 + 1/abs(1 - 1/x), '<', x) == \
         Or(And(-oo < x, x < 0),
@@ -409,23 +409,6 @@ def test_isolve_Sets():
         Piecewise((S.EmptySet, n < 0), (Interval(-n, n), True))
 
 
-def test_integer_domain_relational_isolve():
-
-    dom = FiniteSet(0, 3)
-    x = Symbol('x',zero=False)
-    assert isolve((x - 1)*(x - 2)*(x - 4) < 0, x, domain=dom) == Eq(x, 3)
-
-    x = Symbol('x')
-    assert isolve(x + 2 < 0, x, domain=S.Integers) ==\
-        (x <= -3) & (x > -oo) & Eq(x, floor(x))
-    assert isolve(2*x + 3 > 0, x, domain=S.Integers) ==\
-        (x >= -1) & (x < oo) & Eq(x, floor(x))
-    assert isolve((x**2 + 3*x - 2) < 0, x, domain=S.Integers) ==\
-        (x >= -3) & (x <= 0) & Eq(x, floor(x))
-    assert isolve((x**2 + 3*x - 2) > 0, x, domain=S.Integers) ==\
-        ((x >= 1) & (x < oo) & Eq(x, floor(x))) | ((x <= -4) & (x > -oo) & Eq(x, floor(x)))
-
-
 def test_issue_10671_12466():
     assert solveset(sin(y), y, Interval(0, pi)) == FiniteSet(0, pi)
     i = Interval(1, 10)
diff --git a/sympy/solvers/tests/test_solveset.py b/sympy/solvers/tests/test_solveset.py
index 1f231abf06..8819481302 100644
--- a/sympy/solvers/tests/test_solveset.py
+++ b/sympy/solvers/tests/test_solveset.py
@@ -1,4 +1,5 @@
 from sympy.core.containers import Tuple
+from sympy.core.compatibility import ordered
 from sympy.core.function import (Function, Lambda, nfloat, diff)
 from sympy.core.mod import Mod
 from sympy.core.numbers import (E, I, Rational, oo, pi)
@@ -24,7 +25,7 @@
 from sympy.polys.rootoftools import CRootOf
 from sympy.sets.contains import Contains
 from sympy.sets.conditionset import ConditionSet
-from sympy.sets.fancysets import ImageSet, Range
+from sympy.sets.fancysets import ImageSet
 from sympy.sets.sets import (Complement, EmptySet, FiniteSet,
     Intersection, Interval, Union, imageset, ProductSet)
 from sympy.simplify import simplify
@@ -1700,6 +1701,31 @@ def test_solve_nonlinear_trans():
     assert nonlinsolve([x**2 - y**2/exp(x)], [x, y]) == soln4
 
 
+def test_issue_19050():
+    # test_issue_19050 --> TypeError removed
+    assert dumeq(nonlinsolve([x + y, sin(y)], [x, y]),
+        FiniteSet((ImageSet(Lambda(n, -2*n*pi), S.Integers), ImageSet(Lambda(n, 2*n*pi), S.Integers)),\
+             (ImageSet(Lambda(n, -2*n*pi - pi), S.Integers), ImageSet(Lambda(n, 2*n*pi + pi), S.Integers))))
+    assert dumeq(nonlinsolve([x + y, sin(y) + cos(y)], [x, y]),
+        FiniteSet((ImageSet(Lambda(n, -2*n*pi - 3*pi/4), S.Integers), ImageSet(Lambda(n, 2*n*pi + 3*pi/4), S.Integers)), \
+            (ImageSet(Lambda(n, -2*n*pi - 7*pi/4), S.Integers), ImageSet(Lambda(n, 2*n*pi + 7*pi/4), S.Integers))))
+
+
+def test_issue_16618():
+    # AttributeError is removed !
+    # have to remove the redundancy
+    _n = Dummy('n')
+    eqn = [sin(x)*sin(y), cos(x)*cos(y) - 1]
+    ans = FiniteSet((x, 2*n*pi), (2*n*pi, y), (x, 2*n*pi + pi), (2*n*pi + pi, y),\
+        (x, 2*_n*pi), (2*_n*pi, y), (x, 2*_n*pi + pi), (2*_n*pi + pi, y))
+    sol = nonlinsolve(eqn, [x, y])
+
+    for i0, j0 in zip(ordered(sol), ordered(ans)):
+        assert len(i0) == len(j0) == 2
+        assert all(a.dummy_eq(b) for a, b in zip(i0, j0))
+    assert len(sol) == len(ans)
+
+
 def test_issue_5132_1():
     system = [sqrt(x**2 + y**2) - sqrt(10), x + y - 4]
     assert nonlinsolve(system, [x, y]) == FiniteSet((1, 3), (3, 1))
@@ -1977,32 +2003,6 @@ def test_simplification():
     assert solveset(eq, x, S.Reals) == FiniteSet(S.Half)
 
 
-def test_integer_domain_relational():
-    eq1 = 2*x + 3 > 0
-    eq2 = x**2 + 3*x - 2 >= 0
-    eq3 = x + 1/x > -2 + 1/x
-    eq4 = x + sqrt(x**2 - 5) > 0
-    eq = x + 1/x > -2 + 1/x
-    eq5 = eq.subs(x,log(x))
-    eq6 = log(x)/x <= 0
-    eq7 = log(x)/x < 0
-    eq8 = x/(x-3) < 3
-    eq9 = x/(x**2-3) < 3
-
-    assert solveset(eq1, x, S.Integers) == Range(-1, oo, 1)
-    assert solveset(eq2, x, S.Integers) == Union(Range(-oo, -3, 1), Range(1, oo, 1))
-    assert solveset(eq3, x, S.Integers) == Union(Range(-1, 0, 1), Range(1, oo, 1))
-    assert solveset(eq4, x, S.Integers) == Range(3, oo, 1)
-    assert solveset(eq5, x, S.Integers) == Range(2, oo, 1)
-    assert solveset(eq6, x, S.Integers) == Range(1, 2, 1)
-    assert solveset(eq7, x, S.Integers) == S.EmptySet
-    assert solveset(eq8, x, domain=Range(0,5)) == Range(0, 3, 1)
-    assert solveset(eq9, x, domain=Range(0,5)) == Union(Range(0, 2, 1), Range(2, 5, 1))
-
-    # test_issue_19794
-    assert solveset(x + 2 < 0, x, S.Integers) == Range(-oo, -2, 1)
-
-
 def test_issue_10555():
     f = Function('f')
     g = Function('g')