Révision 109 pobysoPythonSage/src/sageSLZ/sagePolynomialOperations.sage
| sagePolynomialOperations.sage (revision 109) | ||
|---|---|---|
| 87 | 87 |
|
| 88 | 88 |
# End spo_add_polynomial_coeffs_to_matrix_row |
| 89 | 89 |
|
| 90 |
def spo_get_coefficient_for_monomial(monomialsList, coefficientsList, monomial): |
|
| 91 |
""" |
|
| 92 |
Get, for a polynomial, the coefficient for a given monomial. |
|
| 93 |
The polynomial is given as two lists (monomials and coefficients as |
|
| 94 |
return by the respective methods ; indexes of the two lists must match). |
|
| 95 |
If the monomial is not found, 0 is returned. |
|
| 96 |
""" |
|
| 97 |
monomialIndex = 0 |
|
| 98 |
for mono in monomialsList: |
|
| 99 |
if mono == monomial: |
|
| 100 |
return coefficientsList[monomialIndex] |
|
| 101 |
monomialIndex += 1 |
|
| 102 |
return 0 |
|
| 103 |
# End spo_get_coefficient_for_monomial. |
|
| 104 |
|
|
| 105 |
|
|
| 90 | 106 |
def spo_expression_as_string(powI, powT, powP, powN): |
| 91 | 107 |
""" |
| 92 | 108 |
Computes a string version of the i^k + t^l + p^m + N^n expression for |
| ... | ... | |
| 410 | 426 |
printed in colums of columnsWitdth width. |
| 411 | 427 |
""" |
| 412 | 428 |
pRing = p.parent() |
| 413 |
knownMonomials = [] |
|
| 414 | 429 |
polynomialsList = [] |
| 415 | 430 |
pVariables = p.variables() |
| 416 | 431 |
iVariable = pVariables[0] |
| ... | ... | |
| 494 | 509 |
polynomialAtPower *= p |
| 495 | 510 |
nAtPower /= N |
| 496 | 511 |
# End for pPower loop |
| 497 |
return((knownMonomials, polynomialsList))
|
|
| 512 |
return polynomialsList
|
|
| 498 | 513 |
# End spo_polynomial_to_proto_matrix_2 |
| 499 | 514 |
|
| 500 |
def spo_polynomial_to_polynomials_list_3(p, alpha, N, columnsWidth=0): |
|
| 515 |
def spo_polynomial_to_polynomials_list_3(p, alpha, N, iBound, tBound, \ |
|
| 516 |
columnsWidth=0): |
|
| 501 | 517 |
""" |
| 502 | 518 |
From p, alpha, N build a list of polynomials... |
| 503 | 519 |
TODO: more in depth rationale... |
| ... | ... | |
| 586 | 602 |
polynomialsList.append(currentPolynomial) |
| 587 | 603 |
internalIpower += pIdegree |
| 588 | 604 |
# End for tPower |
| 589 |
# The i^iPower * p^pPower * N^(alpha-pPower) i-shift. |
|
| 590 |
if columnsWidth != 0: |
|
| 591 |
polExpStr = spo_expression_as_string(iPower, \ |
|
| 592 |
0, \ |
|
| 593 |
pPower, \ |
|
| 594 |
alpha-pPower) |
|
| 605 |
# Here we have to choose between a |
|
| 606 |
# i^iPower * p^pPower * N^(alpha-pPower) i-shift and |
|
| 607 |
# i^iPower * i^(d_i(p) * pPower) * N^alpha, depend on which |
|
| 608 |
# coefficient is smallest. |
|
| 609 |
IcurrentExponent = iPower + \ |
|
| 610 |
(pPower * polynomialAtPower.degree(i)) |
|
| 611 |
currentMonomial = pRing(i^(IcurrentExponent)) |
|
| 612 |
currentPolynomial = pRing(i^iPower * nAtPower) * \ |
|
| 613 |
polynomialAtPower |
|
| 614 |
currMonomials = currentPolynomial.monomials() |
|
| 615 |
currCoefficients = currentPolynomial.coefficients() |
|
| 616 |
currentCoefficient = spo_get_coefficient_for_monomial( \ |
|
| 617 |
currMonomials, |
|
| 618 |
currCoefficients, |
|
| 619 |
currentMonomial) |
|
| 620 |
if currentCoefficient > nAtAlpha: |
|
| 621 |
if columnsWidth != 0: |
|
| 622 |
polExpStr = spo_expression_as_string(IcurrentCoefficient, \ |
|
| 623 |
0, \ |
|
| 624 |
0, \ |
|
| 625 |
alpha) |
|
| 595 | 626 |
print "->", polExpStr |
| 596 |
currentExpression = i^iPower * nAtPower |
|
| 597 |
currentPolynomial = pRing(currentExpression) * polynomialAtPower |
|
| 598 |
polynomialsList.append(currentPolynomial) |
|
| 627 |
polynomialsList.append(currentMonomial * nAtAlpha) |
|
| 628 |
else: |
|
| 629 |
if columnsWidth != 0: |
|
| 630 |
polExpStr = spo_expression_as_string(iPower, \ |
|
| 631 |
0, \ |
|
| 632 |
pPower, \ |
|
| 633 |
alpha-pPower) |
|
| 634 |
print "->", polExpStr |
|
| 635 |
polynomialsList.append(currentPolynomial) |
|
| 599 | 636 |
# End for iPower |
| 600 | 637 |
polynomialAtPower *= p |
| 601 | 638 |
nAtPower /= N |
| 602 | 639 |
# End for pPower loop |
| 603 |
return((knownMonomials, polynomialsList))
|
|
| 640 |
return polynomialsList
|
|
| 604 | 641 |
# End spo_polynomial_to_proto_matrix_3 |
| 605 | 642 |
|
| 606 | 643 |
def spo_proto_to_column_matrix(protoMatrixColumns, \ |
Formats disponibles : Unified diff