Load the standard form programs, and the MHD example:

The MHD results for the lie symmetry analysis of the magnetohydrodynamic equations in 3 dimensions. This results in a system of linear PDE in 12 dependent and 12 independent variables.

> read `standard_form-2.0.R3-4/stanform`;

> read `standard_form-2.0.R3-4/mhd.sys`;

THE STANDARD FORM PACKAGE

by Allan D. Wittkopf and Gregory Reid
Core code by A. Wittkopf
Core initial-data routines by G. Reid

RELEASE 2 : August 12, 1993
Copyright 1993 by Allan D. Wittkopf and Gregory Reid

So it starts out with 222 equations

> nops(sys);

The length of the equations shows that there are a fair number of small ones, and some fairly large ones, but none are huge:

> map(length,sys);

Now to run it:

> ans:=standard_form(sys):

Initial State of System:
#OT: 0 #Ez: 0 #NL: 0 #UnC: 222

`******End iteration #1 Time:`.(11.220)
#OT: 42 #Ez: 6 #NL: 0 #UnC: 217

`******End iteration #2 Time:`.(3.971)
#OT: 48 #Ez: 3 #NL: 0 #UnC: 217

`******End iteration #3 Time:`.(4.079)
#OT: 63 #Ez: 10 #NL: 0 #UnC: 158

`******End iteration #4 Time:`.(4.570)
#OT: 78 #Ez: 15 #NL: 0 #UnC: 124

`******End iteration #5 Time:`.(3.150)
#OT: 85 #Ez: 18 #NL: 0 #UnC: 105

`******End iteration #6 Time:`.(2.991)
#OT: 93 #Ez: 18 #NL: 0 #UnC: 72

`******End iteration #7 Time:`.(5.590)
#OT: 96 #Ez: 25 #NL: 0 #UnC: 98

`******End iteration #8 Time:`.(4.900)
#OT: 100 #Ez: 30 #NL: 0 #UnC: 79

`******End iteration #9 Time:`.(6.129)
#OT: 101 #Ez: 35 #NL: 0 #UnC: 88

`******End iteration #10 Time:`.(5.290)
#OT: 102 #Ez: 37 #NL: 0 #UnC: 80

`******End iteration #11 Time:`.(7.091)
#OT: 104 #Ez: 40 #NL: 0 #UnC: 72

`******End iteration #12 Time:`.(5.959)
#OT: 104 #Ez: 42 #NL: 0 #UnC: 72

`******End iteration #13 Time:`.(5.471)
#OT: 105 #Ez: 42 #NL: 0 #UnC: 72

`******End iteration #14 Time:`.(10.100)
#OT: 107 #Ez: 44 #NL: 0 #UnC: 75

`******End iteration #15 Time:`.(9.459)
#OT: 111 #Ez: 42 #NL: 0 #UnC: 77

`******End iteration #16 Time:`.(7.200)
#OT: 113 #Ez: 43 #NL: 0 #UnC: 71

`******End iteration #17 Time:`.(7.869)
#OT: 114 #Ez: 44 #NL: 0 #UnC: 67

`******End iteration #18 Time:`.(6.120)
#OT: 116 #Ez: 41 #NL: 0 #UnC: 53

`******End iteration #19 Time:`.(5.440)
#OT: 118 #Ez: 35 #NL: 0 #UnC: 46

`******End iteration #20 Time:`.(3.961)
#OT: 119 #Ez: 34 #NL: 0 #UnC: 42

`******End iteration #21 Time:`.(6.449)
#OT: 120 #Ez: 38 #NL: 0 #UnC: 43

`******End iteration #22 Time:`.(4.600)
#OT: 124 #Ez: 34 #NL: 0 #UnC: 33

`******End iteration #23 Time:`.(5.080)
#OT: 130 #Ez: 28 #NL: 0 #UnC: 25

`******End iteration #24 Time:`.(5.551)
#OT: 130 #Ez: 30 #NL: 0 #UnC: 11

`******End iteration #25 Time:`.(5.949)
#OT: 131 #Ez: 31 #NL: 0 #UnC: 0

That calculation required 2.37M and 181 CPU sec running on a PII 333. Now we look at it:

> ans;

Now look at any divisions that were performed

> shortenpiv(_pivs);

All are clearly unimportant except the K=1 case, and it would need to be handled in a seperate calculation.

Now we find the initial data:

> id:=initial_data(ans);

So we see we have a 13 parameter group.