Re: [math-fun] Simultaneous solutions of 2 eqns., 2 unknowns
----- Original Message ---- From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Friday, September 26, 2008 1:55:02 PM Subject: [math-fun] Simultaneous solutions of 2 eqns., 2 unknowns I have 2 equations in x & y, each of form trig(x) + P(x,y) = 0 where trig is sin or cos, and P is a real polynomial of degree 3 or 4. ________________________________ In Maple 12:
fsolve({cos(y) = x^4+y^4, sin(x) = x^3+y^3}, {x, y}); {x = 0.9667490675, y = -0.4317536212}
Gene
----- Original Message ----
From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Friday, September 26, 2008 1:55:02 PM Subject: [math-fun] Simultaneous solutions of 2 eqns., 2 unknowns
I have 2 equations in x & y, each of form
trig(x) + P(x,y) = 0
where trig is sin or cos, and P is a real polynomial of degree 3 or 4.
________________________________ In Maple 12:
fsolve({cos(y) = x^4+y^4, sin(x) = x^3+y^3}, {x, y}); {x = 0.9667490675, y = -0.4317536212}
Gene
In Macsyma Minus Infinity: (c9) newton([cos(y) = x^4+y^4,sin(x) = x^3+y^3],[x,y],[1.0d0,-0.5d0]) (d9) [x = 0.96674906753953d0, y = - 0.43175362116676d0]
it kinda hurts to see my good old Mma 4.0 ahh (tounge in cheek) 'Palinised', .. if you'll excuse my French: FindRoot[{Cos[y]==x^4+y^4,Sin[x]==x^3+y^3},{x,1},{y,1},AccuracyGoal->24,MaxI terations->500,WorkingPrecision->36] {x -> 0.966749067539526626535801247923148311, y -> -0.431753621166754055063477739712460707} check : {Cos[y]-(x^4+y^4),Sin[x]-(x^3+y^3)}/. % {0``35.4187, 0``35.4558} and that's good to 10^-35 abouts. ----- Original Message ----- From: "Eugene Salamin" <gene_salamin@yahoo.com> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Saturday, September 27, 2008 12:23 AM Subject: Re: [math-fun] Simultaneous solutions of 2 eqns., 2 unknowns
----- Original Message ----
From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Friday, September 26, 2008 1:55:02 PM Subject: [math-fun] Simultaneous solutions of 2 eqns., 2 unknowns
I have 2 equations in x & y, each of form
trig(x) + P(x,y) = 0
where trig is sin or cos, and P is a real polynomial of degree 3 or 4.
________________________________ In Maple 12:
fsolve({cos(y) = x^4+y^4, sin(x) = x^3+y^3}, {x, y}); {x = 0.9667490675, y = -0.4317536212}
Gene
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Eugene Salamin -
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