Program Output

This is one of three inter-related files. To locate the other two files, access Three Surface Intersection Problem.

The program was run twice with two different sets of a, b, c, d, e data. The output for the first run is Section One below; there were six solutions of System D, none of which were solutions for System B. The output for the second run is Section Two below; there were two System D solutions and both satisfied System B.

The program was written with a view towards testing the polynomial reduction method; thus, program output is simplistic in design and rather minimal.

Every time a solution is found for System D, the i, j, k loop indices are displayed, then followed by the x1pflt, x2pflt, x3pflt values (i.e., the solution). The next two data displayed are solution_error and basic_set_error. solution_error shows how well the solution satisfies System D (the "polynomial system"). basic_set_error shows how well the solution satisfies System B (the "basic set") and in some cases this will be a large number; thus, such a solution is extraneous with respect to System B.

   
SECTION ONE

Maxima 5.18.0 http://maxima.sourceforge.net
Using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (aka GCL)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
"Use fn1:simplode([maxpath, file-name-in-dbl-quotes])\; etc., to create in
fn1 a file name"

(%i1) /* Three surface program Test Case 1.wpd    November 10, 2011 (3:03AM)  */

/* begin one time code */

a[1]:2$   a[2]:6$   a[3]:1$
b[1]:-9$  b[2]:4$   b[3]:-6$
c[1]:-3$  c[2]:8$   c[3]:-9$
d[1]:4$   d[2]:5$   d[3]:7$
e1  :2$   e2  :2.8$ e3  :5.4$

--Balance of program listing (and associated statement numbers) deleted--

(%i32) 
(%o33) "Equations eq1, eq2, eq3 follow:"
(%i34) 
(%o34)
20*x3^2+12*x3+x2*(-96*x3-144)+x1*(-144*x3+192*x2-696)+48*x2^2+128*x1^2
              -1839
(%i35) 
(%o35) (102900*x3^2+x1*(385000*x3+110000*x2+2392800)+x2*(70000*x3+656000)
                   +1512000*x3-9600*x2^2+282900*x1^2+3623216)
        /625
(%i36) 
(%o36) (623100*x3^2+x1*(560000*x3-105000*x2+1136900)+2526200*x3
                   +x2*(-240000*x3-260300)+5600*x2^2+105600*x1^2+526761)
        /625
(%i37) 
(%i38) 
(%i39) 
"x1eq follows"

4.1330677279253044E+113*x1^16+3.4816177638165769E+115*x1^15
                             +9.5207986699337984E+116*x1^14
                             +1.088049147573676E+118*x1^13
                             +4.0372335247515427E+118*x1^12
                             -2.8088674285340226E+119*x1^11
                             -3.6721720106422438E+120*x1^10
                             -1.4704989543772044E+121*x1^9
                             -6.5480770692093099E+120*x1^8
                             +1.4992496645586712E+122*x1^7
                             +4.9798669198946339E+122*x1^6
                             +2.4535454592141987E+122*x1^5
                             -1.7705595453732661E+123*x1^4
                             -3.3755178557825277E+123*x1^3
                             +1.6329215110953E+120*x1^2
                             +4.4160212507051009E+123*x1
                             +2.323589376673053E+123

(%i40) 
(%i41) 
(%o42) "Show solutions for the polynomial system"
(%i43) 
"x2eq follows"

-1.5116048179098621E+89*x2^4-2.4669399315392145E+91*x2^3
                            +1.8433697584572433E+94*x2^2
                           
-1.4139077544254316E+96*x2+2.5287228946699688E+97

i = 1

nmbr_x2roots = 4

"x2eq follows"

-1.5116048179098621E+89*x2^4-5.0946591076946017E+90*x2^3
                            +1.7474971223306917E+93*x2^2
                           
-4.5298107876566169E+94*x2+2.4360500183212742E+95

i = 2

nmbr_x2roots = 4

i = 2

j = 3

k = 1

x1pflt = -18.00183546310291

x2pflt = 21.81927785230801

x3pflt = 5.672693971078843

solution_error = 4.9511023221242264E-6

basic_set_error = 82.48486975990423

"x2eq follows"

-1.5116048179098621E+89*x2^4+4.0660365335241104E+90*x2^3
                            -7.4669028173405442E+91*x2^2
                           
+4.5953614875020498E+92*x2-4.1470405336221688E+92

i = 3

nmbr_x2roots = 2

i = 3

j = 2

k = 2

x1pflt = -5.559397575911135

x2pflt = 7.78733742935583

x3pflt = 3.803053039591759

solution_error = 2.0099677562970053E-7

basic_set_error = 34.63232557644681

"x2eq follows"

-1.5116048179098621E+89*x2^4+4.0904011757632389E+90*x2^3
                            -7.442580621995423E+91*x2^2
                           
+4.4656525009345349E+92*x2-3.7072093595402995E+92

i = 4

nmbr_x2roots = 2

"x2eq follows"

-1.5116048179098621E+89*x2^4+5.1409560688342387E+90*x2^3
                            -3.8255990187676112E+91*x2^2
                           
-1.2611058824083709E+92*x2+6.7288623013850759E+92

i = 5

nmbr_x2roots = 4

i = 5

j = 3

k = 1

x1pflt = -4.099397148471326

x2pflt = 15.89904746459797

x3pflt = 0.54241102328524

solution_error = 1.8403425583493835E-6

basic_set_error = 42.17703830759238

"x2eq follows"

-1.5116048179098621E+89*x2^4+7.6554097707741201E+90*x2^3
                            +2.5218225849857932E+92*x2^2
                           
+2.5125216800037992E+92*x2-1.5073731397125987E+93

i = 6

nmbr_x2roots = 4

i = 6

j = 2

k = 2

x1pflt = -0.68416153406724

x2pflt = -3.196148897986859

x3pflt = -0.16304807597771

solution_error = 7.1063968203207986E-7

basic_set_error = 39.42394086929675

"x2eq follows"

-1.5116048179098621E+89*x2^4+9.087086028306474E+90*x2^3
                            +5.460388281056032E+92*x2^2
                           
+3.1947578902781098E+93*x2+1.0444426345206805E+93

i = 7

nmbr_x2roots = 4

"x2eq follows"

-1.5116048179098621E+89*x2^4+9.5896803415416726E+90*x2^3
                            +6.713075539309518E+92*x2^2
                           
+4.9468725753689177E+93*x2+4.4490751192180965E+93

i = 8

nmbr_x2roots = 4

"x2eq follows"

-1.5116048179098621E+89*x2^4+1.0314153927999219E+91*x2^3
                            +8.7209625281734618E+92*x2^2
                           
+8.2660005554499686E+93*x2+1.3088514201687517E+94

i = 9

nmbr_x2roots = 4

i = 9

j = 1

k = 1

x1pflt = 2.927055378910154

x2pflt = -41.07100304448977

x3pflt = -19.40053169103339

solution_error = 7.9548948135751705E-6

basic_set_error = 170.3844219969379

"x2eq follows"

-1.5116048179098621E+89*x2^4+1.3010044619697781E+91*x2^3
                            +1.8289751452980222E+93*x2^2
                            +3.093253347372138E+94*x2+1.1265173828201661E+95

i = 10

nmbr_x2roots = 4

i = 10

j = 3

k = 1

x1pflt = 6.588726260233671

x2pflt = -5.148092913907021

x3pflt = -8.703912747558206

solution_error = 2.8609446729543209E-6

basic_set_error = 55.47286469545191

(%i44) 
case_cntr = 72

Sbound = 1.0000000000000001E-9

(%o45) "end of run"
(%i46)

SECTION TWO

Maxima 5.18.0 http://maxima.sourceforge.net
Using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (aka GCL)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
"Use fn1:simplode([maxpath, file-name-in-dbl-quotes])\; etc., to create in
fn1 a file name"

(%i1) /* Three surface program Test Case 2.wpd    November 10, 2011 (3:03AM)  */

/* begin one time code */

a[1]:-1.03$   a[2]:2$        a[3]:-0.01$
b[1]:-1$      b[2]:0$        b[3]:0$
c[1]:1$       c[2]:0.01$     c[3]:0.04$
d[1]:1.01$    d[2]:0.02$     d[3]:2$
e1  :3.9$     e2  :4.1$      e3  :8.4$

--Balance of program listing (and associated statement numbers) deleted-- 

(%i32) 
(%o33) "Equations eq1, eq2, eq3 follow:"
(%i34) 
(%o34) -(6083360000*x3^2-243332800*x3+x2*(-320000*x3-60833200)
                       
+x1*(-64000000*x3-16000000*x2+1360000)+6083960000*x2^2
                        +4484000000*x1^2-17045238889)
        /100000000
(%i35) 
(%o35) -(67239600*x3^2+x2*(160000*x3-101992000)+509960*x3
                      +x1*(-2400*x3+480000*x2+136009880)+51240000*x2^2
                      +67236400*x1^2-95297001)
        /1000000
(%i36) 
(%o36) -(366210000*x3^2-746068800*x3+x1*(-980000*x3-5000*x2-928117800)
                      
+x2*(-980000*x3-12862800)+462247500*x2^2+462247500*x1^2
                       -845811859)
        /6250000
(%i37) 
(%i38) 
(%i39) 
"x1eq follows"

9.539870758870685E+281*x1^16-3.7765086630154793E+282*x1^15
                            +9.6603201487019756E+283*x1^14
                            -2.5557056703846289E+284*x1^13
                            +3.7986141330916184E+285*x1^12
                            -6.6573583583257668E+285*x1^11
                            +9.1306619965221758E+286*x1^10
                            -1.0999751539948712E+287*x1^9
                            +1.536520659347158E+288*x1^8
                            -8.7152655362035653E+287*x1^7
                            +1.4763102552535207E+289*x1^6
                            -1.0684586470257733E+288*x1^5
                            +1.0723466647490371E+290*x1^4
                            +4.6548729522209408E+289*x1^3
                            -1.4233282746449918E+290*x1^2
                            -2.7228272840659548E+289*x1
                            +4.5523732387273018E+289

(%i40) 
(%i41) 
(%o42) "Show solutions for the polynomial system"
(%i43) 
"x2eq follows"

1.6753846674658863E+103*x2^4+1.0087515618371521E+104*x2^3
                            +5.7411516886132255E+104*x2^2
                           
+2.1069927573669284E+104*x2+1.262983194020069E+103

i = 1

nmbr_x2roots = 2

"x2eq follows"

1.6753846674658863E+103*x2^4+1.00874735111057E+104*x2^3
                            +5.7381873973756773E+104*x2^2
                            +2.0981685226902E+104*x2+1.0812746361487799E+103

i = 2

nmbr_x2roots = 2

i = 2

j = 2

k = 2

x1pflt = -0.85428428137675

x2pflt = -0.061900383327156

x3pflt = 1.518878292758018

solution_error = 7.485131814593818E-8

basic_set_error = 6.0992575567163715E-10

"x2eq follows"

1.6753846674658863E+103*x2^4+1.0013533796888142E+104*x2^3
                            +9.5457384851200266E+103*x2^2
                            -1.2002239743384144E+105*x2
                            +1.1612294155314822E+105

i = 3

nmbr_x2roots = 2

i = 3

j = 2

k = 1

x1pflt = 0.6941764797084

x2pflt = 1.552698559593409

x3pflt = -0.2095697154291

solution_error = 1.2095959998930184E-7

basic_set_error = 1.0138076272370094E-9

"x2eq follows"

1.6753846674658863E+103*x2^4+1.0013417282743036E+104*x2^3
                            +9.4770091662776258E+103*x2^2
                            -1.2022273641734427E+105*x2
                            +1.1689456122146154E+105

i = 4

nmbr_x2roots = 0

(%i44) 
case_cntr = 12

Sbound = 1.0000000000000001E-9

(%o45) "end of run"
(%i46)
  
Home

Rev. 11/11/11 g