Révision 79 pobysoPythonSage/src/sageSLZ/sageSLZ.sage
| sageSLZ.sage (revision 79) | ||
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return([fff, scaledLowerBoundSa, scaledUpperBoundSa, \ |
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fff(scaledLowerBoundSa), fff(scaledUpperBoundSa)]) |
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def slz_float_poly_of_float_to_rat_poly_of_rat(polyOfFloat): |
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# Create a polynomial over the rationals. |
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polynomialRing = QQ[str(polyOfFloat.variables()[0])] |
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return(polynomialRing(polyOfFloat)) |
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# End slz_float_poly_of_float_to_rat_poly_of_rat |
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def slz_get_intervals_and_polynomials(functionSa, variableNameSa, degreeSa, |
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lowerBoundSa, |
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upperBoundSa, floatingPointPrecSa, |
| ... | ... | |
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The initial interval is, possibly, splitted into smaller intervals. |
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It return a list of tuples, each made of: |
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- a first polynomial (without the changed variable f(x) = p(x-x0)); |
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- a second polynomila (with a changed variable f(x) = q(x))
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- a second polynomial (with a changed variable f(x) = q(x))
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- the approximation interval; |
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- the center, x0, of the interval; |
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- the corresponding approximation error. |
| ... | ... | |
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Compute the Sage version of the Taylor polynomial and it's |
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companion data (interval, center...) |
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The input parameter is a five elements tuple: |
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- [0]: the polyomial (without variable change); |
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- [1]: the polyomial (with variable change done in Sollya); |
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- [0]: the polyomial (without variable change), as polynomial over a |
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real ring; |
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- [1]: the polyomial (with variable change done in Sollya), as polynomial |
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over a real ring; |
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- [2]: the interval (as Sollya range); |
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- [3]: the interval center; |
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- [4]: the approximation error. |
| ... | ... | |
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return((polynomialSa, polynomialChangedVarSa, intervalSa, centerSa, errorSa)) |
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# End slz_polynomial_and_interval_to_sage |
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def slz_rat_poly_of_int_to_int_poly_of_int(ratPolyOfInt): |
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pass |
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# End slz_ratPoly_of_int_to_int_poly_of_int |
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def slz_rat_poly_of_rat_to_rat_poly_of_int(ratPolyOfRat, |
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precision): |
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""" |
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Makes a variable substitution into the input polynomial so that the output |
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polynomial can take integer arguments. |
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All variables of the input polynomial "have precision p". That is to say |
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that they are rationals with denominator == 2^precision: x = y/2^precision |
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We "incorporate" these denominators into the coefficients with, |
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respectively, the "right" power. |
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""" |
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polynomialField = ratPolyOfRat.parent() |
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polynomialVariable = rationalPolynomial.variables()[0] |
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print "The polynomial field is:", polynomialField |
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return \ |
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polynomialField(rationalPolynomial.subs({polynomialVariable : \
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polynomialVariable/2^(precision-1)})) |
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# Return a tuple: |
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# - the bivariate integer polynomial in (i,j); |
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# - 2^K |
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# End slz_rat_poly_of_rat_to_rat_poly_of_int |
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print "sageSLZ loaded..." |
Formats disponibles : Unified diff