| 1 | from sage.libs.singular.letterplace import temporary_MPolynomialRing_from_letterplace_ring |
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| 2 | from sage.libs.singular.function import singular_function |
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| 3 | from sage.algebras.free_algebra import FreeAlgebra |
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| 4 | from sage.libs.singular.function import lib, singular_function |
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| 5 | from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing |
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| 6 | |
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| 7 | def iter_free_monomial(monomial, gens): |
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| 8 | for (index, exponent) in monomial: |
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| 9 | for i in xrange(exponent): |
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| 10 | yield gens[index] |
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| 11 | |
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| 12 | def freegb(ideal, deg_bound): |
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| 13 | """ |
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| 14 | sage: F.<x,y,z> = FreeAlgebra(QQ, 3); F |
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| 15 | Free Algebra on 3 generators (x, y, z) over Rational Field |
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| 16 | sage: l=[2*x*z*x+y*x*y, 3*x*y+x*z] |
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| 17 | sage: freegb(l, 10) |
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| 18 | [3*y*x*z^7*y + y*x*z^8, 3*y*x*z^6*y + y*x*z^7, y*x*z^6*x*z + 314928*y^2*x*z^2*x^5, 3*y*x*z^5*y + y*x*z^6, y*x*z^5*x*z - 17496*y^2*x*z^2*x^4, 3*y*x*z^4*y + y*x*z^5, y*x*z^4*x*z + 972*y^2*x*z^2*x^3, 3*y*x*z^4*x^2*z*y + y*x*z^4*x^2*z^2, 3*y*x*z^3*y + y*x*z^4, y*x*z^3*x*z - 54*y^2*x*z^2*x^2, 3*y*x*z^3*x^2*z^2*y + y*x*z^3*x^2*z^3, 3*y*x*z^3*x^2*z*y + y*x*z^3*x^2*z^2, 3*y*x*z^3*x^3*z*y + y*x*z^3*x^3*z^2, 3*y*x*z^2*y + y*x*z^3, y*x*z^2*x*z + 3*y^2*x*z^2*x, 3*y*x*z^2*x^2*z^3*y + y*x*z^2*x^2*z^4, 3*y*x*z^2*x^2*z^2*y + y*x*z^2*x^2*z^3, y*x*z^2*x^2*z^2*x*z + 3*y^2*x*z^2*x^2*z^2*x, 3*y*x*z^2*x^2*z*y + y*x*z^2*x^2*z^2, 3*y*x*z^2*x^3*z^2*y + y*x*z^2*x^3*z^3, 3*y*x*z^2*x^3*z*y + y*x*z^2*x^3*z^2, 3*y*x*z^2*x^4*z*y + y*x*z^2*x^4*z^2, 3*y*x*z*y + y*x*z^2, x*z*y^6*x*z - 7776*y*x*z^2*x^6, x*z*y^5*x*z - 1296*y*x*z^2*x^5, x*z*y^4*x*z - 216*y*x*z^2*x^4, x*z*y^3*x*z - 36*y*x*z^2*x^3, x*z*y^2*x*z - 6*y*x*z^2*x^2, x*z*y*x*z - y*x*z^2*x, 6*x*z*x - y*x*z, 3*x*y + x*z] |
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| 19 | """ |
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| 20 | lib("freegb.lib") |
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| 21 | free_algebra=ideal[0].parent() |
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| 22 | base_ring = free_algebra.base_ring() |
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| 23 | gens = free_algebra.gens() |
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| 24 | variable_names = [str(g) for g in gens] |
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| 25 | pre_letter_place_ring=PolynomialRing(base_ring, variable_names) |
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| 26 | make_letter_place_ring = singular_function("makeLetterplaceRing") |
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| 27 | ring_wrap = make_letter_place_ring(10, ring=pre_letter_place_ring) |
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| 28 | |
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| 29 | (to_letter_place, from_letter_place) = \ |
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| 30 | temporary_MPolynomialRing_from_letterplace_ring(ring_wrap, |
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| 31 | base_ring, gens, deg_bound |
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| 32 | ) |
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| 33 | |
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| 34 | singular_ring = iter(from_letter_place.keys()).next().parent() |
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| 35 | |
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| 36 | polynomial_list=[] |
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| 37 | for p in ideal: |
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| 38 | sum_p = 0 |
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| 39 | for term in p: |
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| 40 | (coef, monomial) = term |
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| 41 | m = 1 |
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| 42 | for (i,v) in enumerate(iter_free_monomial(monomial, gens)): |
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| 43 | m=m*to_letter_place[v][i] |
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| 44 | m=m*coef |
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| 45 | sum_p = sum_p+m |
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| 46 | polynomial_list.append(sum_p) |
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| 47 | |
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| 48 | |
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| 49 | free_gbasis=singular_function("freeGBasis") |
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| 50 | from sage.libs.singular.option import LibSingularOptions |
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| 51 | libsingular_options = LibSingularOptions() |
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| 52 | bck = int(libsingular_options) |
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| 53 | #letter place needs these options |
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| 54 | libsingular_options['redTail'] = True |
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| 55 | libsingular_options['redSB'] = True |
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| 56 | libsingular_options(bck) |
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| 57 | |
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| 58 | singular_system=singular_function("system") |
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| 59 | gb = singular_system("freegb", |
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| 60 | singular_ring.ideal(polynomial_list), |
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| 61 | deg_bound, |
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| 62 | len(gens)) |
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| 63 | |
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| 64 | result = [] |
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| 65 | def sort_key(index_generator_tuple): |
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| 66 | return index_generator_tuple[0] |
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| 67 | for p in gb: |
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| 68 | sum_p=free_algebra(0) |
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| 69 | for (coef, monomial) in p: |
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| 70 | m=free_algebra(1) |
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| 71 | index_generator_list=[] |
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| 72 | for v in monomial.variables(): |
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| 73 | #there exist no exponent > 1 in the result freegb |
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| 74 | (index, alg_gen) = from_letter_place[v] |
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| 75 | index_generator_list.append((index, alg_gen)) |
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| 76 | index_generator_list = sorted(index_generator_list, key=sort_key) |
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| 77 | |
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| 78 | for (index, alg_gen) in index_generator_list: |
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| 79 | m = m * alg_gen |
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| 80 | m=coef * m |
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| 81 | sum_p = sum_p + m |
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| 82 | result.append(sum_p) |
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| 83 | return result |
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