The following syntax worked. I would like to know if there is a better way
to do this.
*for sol in sol1:
coleqs = [ sympy.simplify(SR(e1)).subs(sol.lhs(),sol.rhs()) for e1 in
remEqs]
print "coleq:",coleqs*
On Friday, July 5, 2013 12:05:40 PM UTC-7, ramaKunapuli wrote:
>
> Hi,
>
> I have the following code where I am trying to substitute solution to a
> previous equation in variable y into next set of equations in x,y. I would
> like lhs and rhs to be variables as sometime the code might substitute, say
> z into equations containing z,p etc.,
>
> # set the ploynomial ring
> R5=PolynomialRing(QQ, 2, 'xy', order='lp')
> x,y = R5.gens()
> # define ideal
> I5 = (x^2+2*y^2-2,x^2+x*y+y^2-2)*R5;I5
> print "Ideal = ",I5
> # get groebner basis
> B5 = I5.groebner_basis();B5;
> print "Groebner basis",B5;
> first_poly = [(vars,ali) for vars in R5.gens() for ali in B5 if not
> (Set(ali.variables())-Set([vars]))]
> print "DEBUG: ",first_poly
> print "eliminating ",first_poly[0][0]
> print "equation ",first_poly[0][1]
> init1 = first_poly[0][0]
> eq1 = first_poly[0][1]
> var1 = var(init1)
> sol1 = solve(SR(eq1),var1)
> print sol1
> remEqs = Set(B5) - Set([eq1])
> remVars = Set(R5.gens()) - Set([init1])
> for sol in sol1:
> coleq = [(e1.subs(sol)).rhs() for e1 in remEqs ]
> print coleq
>
>
> I get the following output.
>
> Ideal = Ideal (x^2 + 2*y^2 - 2, x^2 + x*y + y^2 - 2) of Multivariate
> Polynomial Ring in x, y over Rational Field
> Groebner basis [x^2 + 2*y^2 - 2, x*y - y^2, y^3 - 2/3*y]
> DEBUG: [(y, y^3 - 2/3*y)]
> eliminating y
> equation y^3 - 2/3*y
> [
> y == -1/3*sqrt(2)*sqrt(3),
> y == 1/3*sqrt(2)*sqrt(3),
> y == 0
> ]
> Traceback (most recent call last): # get groebner basis
> File "", line 1, in <module>
>
> File "/tmp/tmpLpvTDH/___code___.py", line 22, in <module>
> exec compile(u'for sol in sol1:\n coleq = [(e1.subs(sol)).rhs() for
> e1 in remEqs ]\n print coleq
> File "", line 2, in <module>
>
> File "multi_polynomial_libsingular.pyx", line 3203, in
> sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.subs
>
> (sage/rings/polynomial/multi_polynomial_libsingular.cpp:21540)
> File "element.pyx", line 344, in
> sage.structure.element.Element.__getattr__ (sage/structure/element.c:3637)
> File "misc.pyx", line 257, in
> sage.structure.misc.getattr_from_other_class (sage/structure/misc.c:1507)
> AttributeError: 'sage.symbolic.expression.Expression' object has no
> attribute 'iteritems'
>
>
> Thanks so much.
>
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