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***
# Editing this README
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Experimental SageMath code for computing Puiseux series expansions of solutions
of algebraic equations. This implementation is similar to gfun:-algeqtoseries in
Maple. Its highlight compared to other SageMath implementations of the
Newton-Puiseux algorithm is that it supports equations depending on rational
sage: F = y^16-4*y^12*x^6-4*y^11*x^8+y^10*x^10+6*y^8*x^12+8*y^7*x^14+14*y^6*x^16+4*y^5*x^18+y^4*(x^20-4*x^18)-4*y^3*x^20+y^2*x^22+x^24 # p. 140
sage: f = puiseux(F, 2); f
[-x^(3/2) + alg1*x^(7/4) + O(x^(9/4)),
alg01*x^(3/2) + alg2*x^(7/4) + O(x^(9/4))]
sage: f[0].base_ring()
Univariate Quotient Polynomial Ring in alg1 over Rational Field with modulus 16*alg1^4 + 4*alg1^2 + 1
sage: f[1].base_ring()
Univariate Quotient Polynomial Ring in alg2 over Univariate Quotient Polynomial Ring in alg01 over Rational Field with modulus alg01^3 - alg01^2 + alg01 - 1 with modulus 256*alg2^4 - 64*alg01*alg2^2 + 16*alg01^2
sage: G = y^16-2*y^13*x^5-4*y^12*x^6+y^10*x^10+2*y^9*x^11+y^8*(8*x^13+6*x^12)-2*y^6*x^16+y^5*(-4*x^18+2*x^17)+y^4*(-x^20+8*x^19-4*x^18)+y^2*x^22-2*y*x^23+x^2 # p. 144 (not checked)
sage: f = puiseux(G, 2)
sage: f[0]
alg0*x^(1/8) - 1/8*alg0^14*x^(19/4) + O(x^(45/8))
sage: f[0].base_ring()
Univariate Quotient Polynomial Ring in alg0 over Rational Field with modulus alg0^16 + 1
Here one of the coefficients of the expansion vanishes for some of the possible
