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solve/parametrized

parametrize the solutions of a scalar functions of two variables

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

solve(eqn, varlist)

Parameters

eqn

-

single equation in two variables

varlist

-

list of two names applied to a parameter (for example, xt,yt) or two equations of the form xt=x0,yt=y0 giving the parametrization point. The desired name of the parameter to use in the solution (for example, t) appears as an argument to the variable names. Note that t=0 corresponds to x0,y0.

Description

• 

The solve(eqn,varlist) command substitutes y=y0+txx0 into the given function and tries to solve the resulting equation (set equal to zero) for x as a function of t. If successful, this gives a parametrized solution of the original equation, in that fxt,y0+txtx0=0.

  

Note: This command does not find solutions of the form x=at+x0,y=bt+y0.  It can sometimes find parametrized solutions of nonpolynomial equations, and can find non-rational parametrizations of polynomial equations.  To find rational parametrizations of polynomial systems, use the command algcurves[parametrization].

Examples

solveu2+v21,us=1,vs=0

u=s21s2+1,v=2ss2+1

(1)

tacnode2x43x2y+y42y3+y2

tacnode:=2x4+y43x2y2y3+y2

(2)

tacsolsolvetacnode,xt,yt

tacsol:=x=122t2+12t2+13tt4+2,y=12t22t2+12t2+13t4+2,x=122t2+3+12t2+1tt4+2,y=12t22t2+3+12t2+1t4+2

(3)

solvexxyy,xt,yt

x=ⅇtln1tt1,y=tⅇtln1tt1

(4)

References

  

Corless, Robert M. Essential Maple 7. Chap. 3. Springer-Verlag.

  

Hardy, G. H. Pure Mathematics. Cambridge University Press, 1952.

See Also

algcurves[parametrization]

solve

 


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