Changeset 5753:e207e63d5ceb for sage/calculus/desolvers.py

Timestamp:

08/12/07 18:38:20 (6 years ago)

Author:

William Stein <wstein@…>

Branch:

default

Parents:

5644:6b03fe2cf6a5 (diff), 5752:595c003bb14e (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
Use the (diff) links above to see all the changes relative to each parent.

Message:

merge

File:

• sage/calculus/desolvers.py (modified) (6 diffs)

sage/calculus/desolvers.py

@@ -54 +54 @@
 
     EXAMPLES:
-        sage: desolve("x**2*diff(y,x) + 3*y*x = sin(x)/x",["x","y"])
+        sage: desolvers.desolve("x**2*diff(y,x) + 3*y*x = sin(x)/x",["x","y"])
         y=(%c-cos(x))/x^3
 
@@ -81 +81 @@
 
     EXAMPLES:
-        sage: desolve_laplace("diff(f(x),x,2)=2*diff(f(x),x)-f(x)",["x","f"])
+        sage: desolvers.desolve_laplace("diff(f(x),x,2)=2*diff(f(x),x)-f(x)",["x","f"])
         f(x)=x*%e^x*(?%at('diff(f(x),x,1),x=0))-f(0)*x*%e^x+f(0)*%e^x
-        sage: desolve_laplace("diff(f(x),x,2)=2*diff(f(x),x)-f(x)",["x","f"],[0,1,2])
+        sage: desolvers.desolve_laplace("diff(f(x),x,2)=2*diff(f(x),x)-f(x)",["x","f"],[0,1,2])
         f(x)=x*%e^x+%e^x
 
@@ -127 +127 @@
         sage: des=["'diff(x(t),t)=-4*y(t)","'diff(y(t),t)=-x(t)"]
         sage: vars = ["t","x","y"]
-        sage: desolve_system(des,vars)
+        sage: desolvers.desolve_system(des,vars)
         [x(t)=(2*y(0)+x(0))*%e^-(2*t)/2-(2*y(0)-x(0))*%e^(2*t)/2,y(t)=(2*y(0)-x(0))*%e^(2*t)/4+(2*y(0)+x(0))*%e^-(2*t)/4]
         sage: des=["'diff(x(t),t)=-4*y(t)","'diff(y(t),t)=-x(t)"]
         sage: vars = ["t","x","y"]
-        sage: desolve_system(des,vars,[0,270,90])
+        sage: desolvers.desolve_system(des,vars,[0,270,90])
         [x(t)=45*%e^(2*t)+225*%e^-(2*t),y(t)=225*%e^-(2*t)/2-45*%e^(2*t)/2]
         sage: des=["'diff(x(t),t)=-4*y(t)","'diff(y(t),t)=-z(t)","'diff(z(t),t)=-2*x(t)"]
         sage: vars = ["t","x","y","z"]
         sage: ics=[0,270,90,100]
-        sage: desolve_system(des,vars,ics)
+        sage: desolvers.desolve_system(des,vars,ics)
         [x(t)=%e^t*(260*cos(sqrt(3)*t)/3-80*sin(sqrt(3)*t)/sqrt(3))+550*%e^-(2*t)/3,y(t)=%e^t*(85*sin(sqrt(3)*t)/sqrt(3)-5*cos(sqrt(3)*t)/3)+275*%e^-(2*t)/3,z(t)=%e^t*(-90*sin(sqrt(3)*t)/sqrt(3)-250*cos(sqrt(3)*t)/3)+550*%e^-(2*t)/3]
 
@@ -172 +172 @@
     
     EXAMPLES:
-        sage.:. x,y = PolynomialRing(QQ,2,"xy").gens()
-        sage.:. eulers_method(5*x+y-5,0,1,1/2,1)
-         x                    y                  h*f(x,y)
-         0                    1                   -2
-       1/2                   -1                 -7/4
-         1                -11/4                -11/8
         sage: x,y = PolynomialRing(QQ,2,"xy").gens()
-        sage: eulers_method(5*x+y-5,0,1,1/2,1,method="none")
+        sage: desolvers.eulers_method(5*x+y-5,0,1,1/2,1,method="none")
         [[0, 1], [1/2, -1], [1, -11/4], [3/2, -33/8]]
         sage: RR = RealField(sci_not=0, prec=4, rnd='RNDU')
         sage: x,y = PolynomialRing(RR,2,"xy").gens()
-        sage: eulers_method(5*x+y-5,0,1,1/2,1,method="None")
+        sage: desolvers.eulers_method(5*x+y-5,0,1,1/2,1,method="None")
         [[0, 1], [1/2, -1.0], [1, -2.7], [3/2, -4.0]]
-        sage.:. RR = RealField(sci_not=0, prec=4, rnd='RNDU')
-        sage.:. x,y=PolynomialRing(RR,2,"xy").gens()
-        sage.:. eulers_method(5*x+y-5,0,1,1/2,1)
+        sage: RR = RealField(sci_not=0, prec=4, rnd='RNDU')
+        sage: x,y=PolynomialRing(RR,2,"xy").gens()
+        sage: desolvers.eulers_method(5*x+y-5,0,1,1/2,1)
          x                    y                  h*f(x,y)
          0                    1                -2.00
@@ -228 +222 @@
         sage: eulers_method_2x2(f,g, 0, 0, 0, 1/3, 1,method="none")
         [[0, 0, 0], [1/3, 0, 0], [2/3, 1/9, 0], [1, 10/27, 1/27], [4/3, 68/81, 4/27]]
-        sage.:. eulers_method_2x2(f,g, 0, 0, 0, 1/3, 1)
+        sage: desolvers.eulers_method_2x2(f,g, 0, 0, 0, 1/3, 1)
          t                    x                h*f(t,x,y)                    y           h*g(t,x,y)
          0                    0                         0                    0                    0
@@ -234 +228 @@
        2/3                  1/9                      7/27                    0                 1/27
          1                10/27                     38/81                 1/27                  1/9
-        sage.: RR = RealField(sci_not=0, prec=4, rnd='RNDU')
-        sage.: t,x,y=PolynomialRing(RR,3,"txy").gens()
-        sage.: f = x+y+t; g = x-y
-        sage.:. eulers_method_2x2(f,g, 0, 0, 0, 1/3, 1)
+        sage: RR = RealField(sci_not=0, prec=4, rnd='RNDU')
+        sage: t,x,y=PolynomialRing(RR,3,"txy").gens()
+        sage: f = x+y+t; g = x-y
+        sage: eulers_method_2x2(f,g, 0, 0, 0, 1/3, 1)
          t                    x                h*f(t,x,y)                    y           h*g(t,x,y)
          0                    0                     0.000                    0                0.000