Ticket #7797: trac7797-latex_letterplace.patch

sage/algebras/letterplace/free_algebra_element_letterplace.pyx

@@ -224 +224 @@
             return ' '.join(L)
         return '0'
 
+    def _latex_(self):
+        """
+        TEST::
+
+            sage: K.<z> = GF(25)
+            sage: F.<a,b,c> = FreeAlgebra(K, implementation='letterplace', degrees=[1,2,3])
+            sage: -(a*b*(z+1)-c)^2
+            (2*z + 1)*a*b*a*b + (z + 1)*a*b*c + (z + 1)*c*a*b - c*c
+            sage: latex(-(a*b*(z+1)-c)^2)     # indirect doctest
+            \left(2 z + 1\right) a b a b + \left(z + 1\right) a b c + \left(z + 1\right) c a b - c c
+
+        """
+        cdef list L = []
+        cdef FreeAlgebra_letterplace P = self._parent
+        cdef int ngens = P.__ngens
+        from sage.all import latex
+        if P._base.is_atomic_repr():
+            for E,c in zip(self._poly.exponents(),self._poly.coefficients()):
+                monstr = P.exponents_to_latex(E)
+                if monstr:
+                    if c==1:
+                        if L:
+                            L.extend(['+',monstr])
+                        else:
+                            L.append(monstr)
+                    elif c==-1:
+                        if L:
+                            L.extend(['-',monstr])
+                        else:
+                            L.append('-'+monstr)
+                    else:
+                        if L:
+                            if c>=0:
+                                L.extend(['+',repr(latex(c))+' '+monstr])
+                            else:
+                                L.extend(['-',repr(latex(-c))+' '+monstr])
+                        else:
+                            L.append(repr(latex(c))+' '+monstr)
+                else:
+                    if c>=0:
+                        if L:
+                            L.extend(['+',repr(latex(c))])
+                        else:
+                            L.append(repr(latex(c)))
+                    else:
+                        if L:
+                            L.extend(['-',repr(latex(-c))])
+                        else:
+                            L.append(repr(c))
+        else:
+            for E,c in zip(self._poly.exponents(),self._poly.coefficients()):
+                monstr = P.exponents_to_latex(E)
+                if monstr:
+                    if c==1:
+                        if L:
+                            L.extend(['+',monstr])
+                        else:
+                            L.append(monstr)
+                    elif c==-1:
+                        if L:
+                            L.extend(['-',monstr])
+                        else:
+                            L.append('-'+monstr)
+                    else:
+                        if L:
+                            L.extend(['+','\\left('+repr(latex(c))+'\\right) '+monstr])
+                        else:
+                            L.append('\\left('+repr(latex(c))+'\\right) '+monstr)
+                else:
+                    if L:
+                        L.extend(['+',repr(latex(c))])
+                    else:
+                        L.append(repr(latex(c)))
+        if L:
+            return ' '.join(L)
+        return '0'
+
     def degree(self):
         """
         Return the degree of this element.

sage/algebras/letterplace/free_algebra_letterplace.pxd

@@ -25 +25 @@
     cdef object __monoid
     cdef public object __custom_name
     cdef str exponents_to_string(self, E)
+    cdef str exponents_to_latex(self, E)
     cdef tuple _degrees

sage/algebras/letterplace/free_algebra_letterplace.pyx

@@ -451 +451 @@
         """
         return "Free Associative Unital Algebra on %d generators %s over %s"%(self.__ngens-self._nb_slackvars,self.gens(),self._base)
 
+    def _latex_(self):
+        """
+        Representation of this free algebra in LaTeX.
+
+        EXAMPLE::
+
+            sage: F.<bla,alpha,z> = FreeAlgebra(QQ, implementation='letterplace', degrees=[1,2,3])
+            sage: latex(F)
+            \Bold{Q}\langle \mbox{bla}, \alpha, z\rangle
+
+        """
+        from sage.all import latex
+        return "%s\\langle %s\\rangle"%(latex(self.base_ring()),', '.join(self.latex_variable_names()))
+
     def degbound(self):
         """
         Return the degree bound that is currently used.
@@ -604 +618 @@
             #    out.append(s)
         return '*'.join(out)
 
+    # Auxiliar methods
+    cdef str exponents_to_latex(self, E):
+        """
+        This auxiliary method is used for the representation of elements of this free algebra as a latex string.
+
+        EXAMPLE::
+
+            sage: K.<z> = GF(25)
+            sage: F.<a,b,c> = FreeAlgebra(K, implementation='letterplace', degrees=[1,2,3])
+            sage: -(a*b*(z+1)-c)^2
+            (2*z + 1)*a*b*a*b + (z + 1)*a*b*c + (z + 1)*c*a*b - c*c
+            sage: latex(-(a*b*(z+1)-c)^2)     # indirect doctest
+            \left(2 z + 1\right) a b a b + \left(z + 1\right) a b c + \left(z + 1\right) c a b - c c
+
+        """
+        cdef int ngens = self.__ngens
+        cdef int nblocks = len(E)/ngens
+        cdef int i,j,base, exp, var_ind
+        cdef list out = []
+        cdef list tmp
+        cdef list names = self.latex_variable_names()
+        for i from 0<=i<nblocks:
+            base = i*ngens
+            tmp = [(j,E[base+j]) for j in xrange(ngens) if E[base+j]]
+            if not tmp:
+                continue
+            var_ind, exp = tmp[0]
+            if len(tmp)>1 or exp>1:
+                raise NotImplementedError, "\n  Apparently you tried to view the letterplace algebra with\n  shift-multiplication as the free algebra over a finitely\n  generated free abelian monoid.\n  In principle, this is correct, but it is not implemented, yet."
+
+            out.append(names[var_ind])
+            i += (self._degrees[var_ind]-1)
+        return ' '.join(out)
+
     def _reductor_(self, g, d):
         """
         Return a commutative ideal that can be used to compute the normal