Coverage for local/lib/python2.7/site-packages/sage/tests/french_book/float_doctest.py : 0%

## -*- encoding: utf-8 -*- 

""" 

This file (./float_doctest.sage) was *autogenerated* from ./float.tex, 

with sagetex.sty version 2011/05/27 v2.3.1. 

It contains the contents of all the sageexample environments from this file. 

You should be able to doctest this file with: 

sage -t ./float_doctest.sage 

It is always safe to delete this file; it is not used in typesetting your 

document. 

Sage example in ./float.tex, line 127:: 

sage: xrdf = RDF(3.0) 

Sage example in ./float.tex, line 137:: 

sage: R100 = RealField(100) # précision : 100 bits. 

sage: x100 = R100(3/8); x100 

0.37500000000000000000000000000 

Sage example in ./float.tex, line 148:: 

sage: Rdefaut = RealField() # précision par défaut de 53 bits 

sage: xdefaut = Rdefaut(2/3) 

Sage example in ./float.tex, line 154:: 

sage: xrdf.prec() 

53 

sage: x100.prec() 

100 

sage: xdefaut.prec() 

53 

Sage example in ./float.tex, line 168:: 

sage: x = 1.0; print(type(x)) 

<type 'sage.rings.real_mpfr.RealLiteral'> 

sage: x.prec() 

53 

Sage example in ./float.tex, line 182:: 

sage: x = 1.0 # x appartient à RealField() 

sage: x = 0.1e+1 # idem : x appartient à RealField() 

sage: x = 1 # x est entier 

sage: x = RDF(1) # x est un flottant double précision machine 

sage: x = RDF(1.) # idem : x est un flottant double précision 

sage: x = RDF(0.1e+1) # idem 

sage: x = 4/3 # x est un nombre rationnel 

sage: R = RealField(20) 

sage: x = R(1) # x est un flottant de précision 20 bits 

Sage example in ./float.tex, line 194:: 

sage: RDF(8/3) 

2.6666666666666665 

sage: R100 = RealField(100); R100(8/3) 

2.6666666666666666666666666667 

Sage example in ./float.tex, line 202:: 

sage: x = R100(8/3) 

sage: R = RealField(); R(x) 

2.66666666666667 

sage: RDF(x) 

2.6666666666666665 

Sage example in ./float.tex, line 216:: 

sage: 1.0/0.0 

+infinity 

sage: RDF(1)/RDF(0) 

+infinity 

sage: RDF(-1.0)/RDF(0.) 

-infinity 

Sage example in ./float.tex, line 225:: 

sage: 0.0/0.0 

NaN 

sage: RDF(0.0)/RDF(0.0) 

NaN 

Sage example in ./float.tex, line 256:: 

sage: R2 = RealField(2) 

Sage example in ./float.tex, line 303:: 

sage: x2 = R2(1.); x2.ulp() 

0.50 

sage: xr = 1.; xr.ulp() 

2.22044604925031e-16 

Sage example in ./float.tex, line 356:: 

sage: a = 10000.0; b = 9999.5; c = 0.1; c 

0.100000000000000 

sage: a1 = a+c # on perturbe a 

sage: a1-b 

0.600000000000364 

Sage example in ./float.tex, line 373:: 

sage: a = 1.0; b = 10.0^4; c = 1.0 

sage: delta = b^2-4*a*c 

sage: x = (-b-sqrt(delta))/(2*a); y = (-b+sqrt(delta))/(2*a) 

sage: x, y 

(-9999.99990000000, -0.000100000001111766) 

Sage example in ./float.tex, line 382:: 

sage: x+y+b/a 

0.000000000000000 

sage: x*y-c/a 

1.11766307320238e-9 

Sage example in ./float.tex, line 394:: 

sage: y = (c/a)/x; y 

-0.000100000001000000 

sage: x+y+b/a 

0.000000000000000 

Sage example in ./float.tex, line 410:: 

sage: x1 = R2(1/2); x2 = R2(4); x3 = R2(-4) 

sage: x1, x2, x3 

(0.50, 4.0, -4.0) 

sage: x1+(x2+x3) 

0.50 

sage: (x1+x2)+x3 

0.00 

Sage example in ./float.tex, line 431:: 

sage: x = RDF(1/3) 

sage: for i in range(1,100): x = 4*x-1; print(x) 

0.333333333333 

0.333333333333 

0.333333333333 

... 

-1.0 

-5.0 

-21.0 

-85.0 

-341.0 

-1365.0 

-5461.0 

-21845.0 

... 

Sage example in ./float.tex, line 461:: 

sage: x = RDF(1/2) 

sage: for i in range(1,100): x = 3*x-1; print(x) 

0.5 

0.5 

0.5 

... 

0.5 

Sage example in ./float.tex, line 484:: 

sage: x = RDF(1/3) 

Sage example in ./float.tex, line 488:: 

sage: x = 1/3 

Sage example in ./float.tex, line 545:: 

sage: def sumharmo(P): 

....: RFP = RealField(P) 

....: y = RFP(1.); x = RFP(0.); n = 1 

....: while x != y: 

....: y = x; x += 1/n; n += 1 

....: return P, n, x 

Sage example in ./float.tex, line 556:: 

sage: sumharmo(2) 

(2, 5, 2.0) 

sage: sumharmo(20) 

(20, 131073, 12.631) 

Sage example in ./float.tex, line 590:: 

sage: def iter(y,delta,a,n): 

....: for i in range(0,n): 

....: y += delta 

....: delta *= a 

....: return y 

Sage example in ./float.tex, line 600:: 

sage: def exact(y,delta,a,n): 

....: return y+delta*(1-a^n)/(1-a) 

Sage example in ./float.tex, line 608:: 

sage: y0 = RDF(10^13); delta0 = RDF(1); a = RDF(1-10^(-8)); n = 100000 

sage: ii = iter(y0,delta0,a,n) 

sage: s = exact(10^13,1,1-10^(-8),n) 

sage: print("exact - sommation classique: {}".format(s-ii)) # abs tol 0.1 

exact - sommation classique: -45.5 

Sage example in ./float.tex, line 618:: 

sage: def sumcomp(y,delta,e,n,a): 

....: for i in range(0,n): 

....: b = y 

....: e += delta 

....: y = b+e 

....: e += (b-y) 

....: delta = a*delta # nouvelle valeur de delta 

....: return y 

Sage example in ./float.tex, line 662:: 

sage: c = sumcomp(y0,delta0,RDF(0.0),n,a) 

sage: print("exact-sommation compensee: {}".format(s-c)) 

exact-sommation compensee: 0.0 

Sage example in ./float.tex, line 681:: 

sage: x = CDF(2,1.); x 

2.0 + 1.0*I 

sage: y = CDF(20,0); y 

20.0 

Sage example in ./float.tex, line 688:: 

sage: z = ComplexDoubleElement(2.,1.); z 

2.0 + 1.0*I 

Sage example in ./float.tex, line 697:: 

sage: C = ComplexField(); C(2,3) 

2.00000000000000 + 3.00000000000000*I 

sage: C100 = ComplexField(100); C100(2,3) 

2.0000000000000000000000000000 + 3.0000000000000000000000000000*I 

Sage example in ./float.tex, line 714:: 

sage: R200 = RealField(200); R200.pi() 

3.1415926535897932384626433832795028841971693993751058209749 

sage: R200.euler_constant() 

0.57721566490153286060651209008240243104215933593992359880577 

Sage example in ./float.tex, line 723:: 

sage: x = RDF.pi()/2; x.cos() # approximation flottante de zero! 

6.123233995736757e-17 

sage: x.cos().arccos() - x 

0.0 

"""