Revision history [back]
 | 1 | initial version |
The best approach I've found so far is to define an eliminate(vars, eqns) procedure (see below) which attempts to remove all the listed vars from the system, so that:
var('x, y, z') eqns = [ x^2 + y^2 == z, x == y] view(eliminate([x], eqns))
gives [2y^2 == z] and solve(eliminate([x], eqns), z) gives me what I was after originally. But I figure I must be missing something obvious.
| | 2 | forgot my function definition |
The best approach I've found so far is to define an eliminate(vars, eqns) procedure (see below) which attempts to remove all the listed vars from the system, so that:
var('x, y, z') eqns = [ x^2 + y^2 == z, x == y] view(eliminate([x], eqns))
gives [2y^2 == z] and solve(eliminate([x], eqns), z) gives me what I was after originally. But I figure I must be missing something obvious.
def eliminate(vars, eqns): """Eliminate the listed variables from the system of equations""" if type(vars) is not list: vars = [vars] if type(eqns) is not list: eqns = [eqns]
# for each variable to be eliminated,
# look for an equation that contains it
# and that we can solve uniquely for it
for var in vars:
soln = None
for eqn in eqns:
if var in eqn.args():
soln = solve(eqn,var)
if len(soln) == 1: break
# if we found an equation determining the variable to be eliminated
# substitute its value throughout, and omit the defining equation
if soln:
val = soln[0].rhs()
eqns = [e.subs({var : val}) for e in eqns if e is not eqn]
# give back whatever we ended up with
return eqns| | 3 | No.3 Revision |
The best approach I've found so far is to define an eliminate(vars, eqns) procedure (see below) which attempts to remove all the listed vars from the system, so that:
var('x, y, z') eqns = [ x^2 + y^2 == z, x == y] view(eliminate([x], eqns))
gives [2y^2 == z] and solve(eliminate([x], eqns), z) gives me what I was after originally. But I figure I must be missing something obvious.
def eliminate(vars, eqns):
"""Eliminate the listed variables from the system of equations"""
if type(vars) is not list: vars = [vars]
if type(eqns) is not list: eqns = [eqns] [eqns]
# for each variable to be eliminated,
# look for an equation that contains it
# and that we can solve uniquely for it
for var in vars:
soln = None
for eqn in eqns:
if var in eqn.args():
soln = solve(eqn,var)
if len(soln) == 1: break
# if we found an equation determining the variable to be eliminated
# substitute its value throughout, and omit the defining equation
if soln:
val = soln[0].rhs()
eqns = [e.subs({var : val}) for e in eqns if e is not eqn]
# give back whatever we ended up with
return eqns
4 No.4 Revision
The best approach I've found so far is to define an eliminate(vars, eqns) procedure (see below) which attempts to remove all the listed vars from the system, so that:
var('x, y, z')
eqns = [ x^2 + y^2 == z, x == y]
view(eliminate([x], eqns))eqns))
gives [2y^2 == z] and solve(eliminate([x], eqns), z) gives me what I was after originally. But I figure I must be missing something obvious.
def eliminate(vars, eqns):
"""Eliminate the listed variables from the system of equations"""
if type(vars) is not list: vars = [vars]
if type(eqns) is not list: eqns = [eqns]
# for each variable to be eliminated,
# look for an equation that contains it
# and that we can solve uniquely for it
for var in vars:
soln = None
for eqn in eqns:
if var in eqn.args():
soln = solve(eqn,var)
if len(soln) == 1: break
# if we found an equation determining the variable to be eliminated
# substitute its value throughout, and omit the defining equation
if soln:
val = soln[0].rhs()
eqns = [e.subs({var : val}) for e in eqns if e is not eqn]
# give back whatever we ended up with
return eqns
