0
$\begingroup$

I have this large equation involving the variables x, y and I need to plot it with all its important features. How? Is there an auto fit/zoom feature?

25448251500000 - 535526010000 x + 5077310000 x^2 - 36775800 x^3 + 
  250890 x^4 - (6199 x^5)/5 + (17 x^6)/5 - x^7/250 + 920347020000 y - 
  16448410100 x y + 122367000 x^2 y - 607718 x^3 y + (15694 x^4 y)/
  5 - (7099 x^5 y)/500 + (9 x^6 y)/250 - (x^7 y)/25000 + 
  15128205050 y^2 - 220083300 x y^2 + 1275939 x^2 y^2 - (
  19598 x^3 y^2)/5 + (8699 x^4 y^2)/1000 - (11 x^5 y^2)/500 + (
  x^6 y^2)/50000 + 152047500 y^3 - 1691358 x y^3 + 7640 x^2 y^3 - (
  96 x^3 y^3)/5 + (13 x^4 y^3)/500 - (x^5 y^3)/25000 + 1032409 y^4 - (
  40191 x y^4)/5 + (119 x^2 y^4)/5 - (11 x^3 y^4)/250 + (x^4 y^4)/
  50000 + (24094 y^5)/5 - (12299 x y^5)/500 + (9 x^2 y^5)/250 - (
  x^3 y^5)/25000 + (14699 y^6)/1000 - (23 x y^6)/500 + (x^2 y^6)/
  50000 + (13 y^7)/500 - (x y^7)/25000 + y^8/50000 + 
  5089650300000 Sin[x] - 107105202000 x Sin[x] + 
  1015462000 x^2 Sin[x] - 7355160 x^3 Sin[x] + 50178 x^4 Sin[x] - 
  6199/25 x^5 Sin[x] + 17/25 x^6 Sin[x] - (x^7 Sin[x])/1250 + 
  133172901000 y Sin[x] - 2218630000 x y Sin[x] + 
  14318780 x^2 y Sin[x] - 47992 x^3 y Sin[x] + 6299/50 x^4 y Sin[x] - 
  9/25 x^5 y Sin[x] + (x^6 y Sin[x])/2500 + 1693912000 y^2 Sin[x] - 
  21830360 x y^2 Sin[x] + 112000 x^2 y^2 Sin[x] - 
  304 x^3 y^2 Sin[x] + 12/25 x^4 y^2 Sin[x] - (x^5 y^2 Sin[x])/1250 + 
  13470380 y^3 Sin[x] - 119968 x y^3 Sin[x] + 408 x^2 y^3 Sin[x] - 
  4/5 x^3 y^3 Sin[x] + (x^4 y^3 Sin[x])/2500 + 71778 y^4 Sin[x] - 
  10199/25 x y^4 Sin[x] + 17/25 x^2 y^4 Sin[x] - (x^3 y^4 Sin[x])/
  1250 + 12299/50 y^5 Sin[x] - 21/25 x y^5 Sin[x] + (x^2 y^5 Sin[x])/
  2500 + 12/25 y^6 Sin[x] - (x y^6 Sin[x])/1250 + (y^7 Sin[x])/2500 ==
  0
$\endgroup$
2
$\begingroup$

Not a complete answer but note that if we take your equation and then simplify we get

eqn = 25448251500000 - 535526010000 x + 5077310000 x^2 - 
    36775800 x^3 + 250890 x^4 - (6199 x^5)/5 + (17 x^6)/5 - x^7/250 + 
    920347020000 y - 16448410100 x y + 122367000 x^2 y - 
    607718 x^3 y + (15694 x^4 y)/5 - (7099 x^5 y)/500 + (9 x^6 y)/
     250 - (x^7 y)/25000 + 15128205050 y^2 - 220083300 x y^2 + 
    1275939 x^2 y^2 - (19598 x^3 y^2)/5 + (8699 x^4 y^2)/
     1000 - (11 x^5 y^2)/500 + (x^6 y^2)/50000 + 152047500 y^3 - 
    1691358 x y^3 + 
    7640 x^2 y^3 - (96 x^3 y^3)/5 + (13 x^4 y^3)/500 - (x^5 y^3)/
     25000 + 1032409 y^4 - (40191 x y^4)/5 + (119 x^2 y^4)/
     5 - (11 x^3 y^4)/250 + (x^4 y^4)/50000 + (24094 y^5)/
     5 - (12299 x y^5)/500 + (9 x^2 y^5)/250 - (x^3 y^5)/
     25000 + (14699 y^6)/1000 - (23 x y^6)/500 + (x^2 y^6)/
     50000 + (13 y^7)/500 - (x y^7)/25000 + y^8/50000 + 
    5089650300000 Sin[x] - 107105202000 x Sin[x] + 
    1015462000 x^2 Sin[x] - 7355160 x^3 Sin[x] + 50178 x^4 Sin[x] - 
    6199/25 x^5 Sin[x] + 17/25 x^6 Sin[x] - (x^7 Sin[x])/1250 + 
    133172901000 y Sin[x] - 2218630000 x y Sin[x] + 
    14318780 x^2 y Sin[x] - 47992 x^3 y Sin[x] + 
    6299/50 x^4 y Sin[x] - 9/25 x^5 y Sin[x] + (x^6 y Sin[x])/2500 + 
    1693912000 y^2 Sin[x] - 21830360 x y^2 Sin[x] + 
    112000 x^2 y^2 Sin[x] - 304 x^3 y^2 Sin[x] + 
    12/25 x^4 y^2 Sin[x] - (x^5 y^2 Sin[x])/1250 + 
    13470380 y^3 Sin[x] - 119968 x y^3 Sin[x] + 408 x^2 y^3 Sin[x] - 
    4/5 x^3 y^3 Sin[x] + (x^4 y^3 Sin[x])/2500 + 71778 y^4 Sin[x] - 
    10199/25 x y^4 Sin[x] + 
    17/25 x^2 y^4 Sin[x] - (x^3 y^4 Sin[x])/1250 + 
    12299/50 y^5 Sin[x] - 
    21/25 x y^5 Sin[x] + (x^2 y^5 Sin[x])/2500 + 
    12/25 y^6 Sin[x] - (x y^6 Sin[x])/1250 + (y^7 Sin[x])/2500 == 0;


eqn1=FullSimplify[eqn]

(-300 + 2 x - y) (24950 + (-300 + x) x + y (100 + y)) (1699950000 + (-200 + x) x (20000 + (-200 + x) x) + y (400 + y) (80000 + y (400 + y))) (100 + y + 20 Sin[x]) == 0

Which is easier to work with. Further we can find solutions for y as follows

sols = Solve[eqn1, y]
{{y -> 2 (-150 + x)},
  {y -> -50 - Sqrt[-22450 + 300 x - x^2]},
  {y -> -50 +  Sqrt[-22450 + 300 x - x^2]}, 
  {y -> -200 - (-99950000 + 4000000 x - 60000 x^2 + 
          400 x^3 - x^4)^(1/4)}, {y -> -200 - 
        I (-99950000 + 4000000 x - 60000 x^2 + 400 x^3 - x^4)^(1/4)},
  {y -> -200 + I (-99950000 + 4000000 x - 60000 x^2 + 400 x^3 - x^4)^(1/4)}, 
  {y -> -200 + (-99950000 + 4000000 x - 60000 x^2 + 400 x^3 - x^4)^(1/4)},
  {y -> -20 (5 + Sin[x])}}

showing that there are seven solutions. Two of which are very simple. Further the original equation may be factored.

Factor[eqn1]

(-300 + 2 x - y) (24950 - 300 x + x^2 + 100 y + y^2) (1699950000 - 4000000 x + 60000 x^2 - 400 x^3 + x^4 + 32000000 y + 240000 y^2 + 800 y^3 + y^4) (100 + y + 20 Sin[x]) == 0

Showing that you have a straight line, a circle, a sine wave and a further contour for which I don't have a name. Bob Hanlon illustrates them nicely. Hope that helps.

$\endgroup$
1
$\begingroup$

You need to tell Mathematica the region for which you have an interest.

ContourPlot[
 25448251500000 - 535526010000 x + 5077310000 x^2 - 36775800 x^3 + 
   250890 x^4 - (6199 x^5)/5 + (17 x^6)/5 - x^7/250 + 920347020000 y - 
   16448410100 x y + 122367000 x^2 y - 
   607718 x^3 y + (15694 x^4 y)/5 - (7099 x^5 y)/500 + (9 x^6 y)/
    250 - (x^7 y)/25000 + 15128205050 y^2 - 220083300 x y^2 + 
   1275939 x^2 y^2 - (19598 x^3 y^2)/5 + (8699 x^4 y^2)/1000 - (11 x^5 y^2)/
    500 + (x^6 y^2)/50000 + 152047500 y^3 - 1691358 x y^3 + 
   7640 x^2 y^3 - (96 x^3 y^3)/5 + (13 x^4 y^3)/500 - (x^5 y^3)/25000 + 
   1032409 y^4 - (40191 x y^4)/5 + (119 x^2 y^4)/5 - (11 x^3 y^4)/
    250 + (x^4 y^4)/50000 + (24094 y^5)/5 - (12299 x y^5)/500 + (9 x^2 y^5)/
    250 - (x^3 y^5)/25000 + (14699 y^6)/1000 - (23 x y^6)/500 + (x^2 y^6)/
    50000 + (13 y^7)/500 - (x y^7)/25000 + y^8/50000 + 5089650300000 Sin[x] - 
   107105202000 x Sin[x] + 1015462000 x^2 Sin[x] - 7355160 x^3 Sin[x] + 
   50178 x^4 Sin[x] - 6199/25 x^5 Sin[x] + 
   17/25 x^6 Sin[x] - (x^7 Sin[x])/1250 + 133172901000 y Sin[x] - 
   2218630000 x y Sin[x] + 14318780 x^2 y Sin[x] - 47992 x^3 y Sin[x] + 
   6299/50 x^4 y Sin[x] - 9/25 x^5 y Sin[x] + (x^6 y Sin[x])/2500 + 
   1693912000 y^2 Sin[x] - 21830360 x y^2 Sin[x] + 112000 x^2 y^2 Sin[x] - 
   304 x^3 y^2 Sin[x] + 12/25 x^4 y^2 Sin[x] - (x^5 y^2 Sin[x])/1250 + 
   13470380 y^3 Sin[x] - 119968 x y^3 Sin[x] + 408 x^2 y^3 Sin[x] - 
   4/5 x^3 y^3 Sin[x] + (x^4 y^3 Sin[x])/2500 + 71778 y^4 Sin[x] - 
   10199/25 x y^4 Sin[x] + 17/25 x^2 y^4 Sin[x] - (x^3 y^4 Sin[x])/1250 + 
   12299/50 y^5 Sin[x] - 21/25 x y^5 Sin[x] + (x^2 y^5 Sin[x])/2500 + 
   12/25 y^6 Sin[x] - (x y^6 Sin[x])/1250 + (y^7 Sin[x])/2500 == 0,
 {x, -50, 250}, {y, -225, -25},
 PlotPoints -> 100,
 MaxRecursion -> 2,
 AspectRatio -> 200/300]

enter image description here

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.