Maple Tools - Symbolic engine for SMath Studio. - Messages
#161 Posted: 6/2/2013 12:01:21 AM
Updated. Animation added.
[albumimg]192[/albumimg] [albumimg]193[/albumimg]

R:=`::R`: # R-radius of the large circle
r:=`::r`: # r-radius of the small circle
N:=`::N`: # N-number of frames of animation
A:=plot([R*cos(t),R*sin(t),t=0..2*Pi],color=blue,thickness=2):
B:=seq(plottools[disk]([(R-r)*cos(2*Pi*k/N),(R-r)*sin(2*Pi*k/N)],r,
color=yellow),k=1..N):
C:=seq(plottools[disk]([(R-r)*cos(2*Pi*k/N)+r*cos(2*Pi*k/N-R*2*Pi*k/r/N),
(R-r)*sin(2*Pi*k/N)+r*sin(2*Pi*k/N-R*2*Pi*k/r/N)],r/15,color=red),k=1..N):
F:=seq(plot([(R-r)*cos(t)+r*cos(t-R*t/r),(R-r)*sin(t)+r*sin(t-R*t/r),
t=0..2*Pi*k/N],x=-R..R,y=-R..R,color=red,thickness=2),k=1..N):
for k from 1 to N do E[k]:=plots[display](A,C[k],B[k],F[k]); od:
plots[display]([seq(E[k],k=1..N)],insequence=true,scaling=constrained,
view=[-R-1..R+1,-R-1..R+1]);
r:=`::r`: # r-radius of the small circle
N:=`::N`: # N-number of frames of animation
A:=plot([R*cos(t),R*sin(t),t=0..2*Pi],color=blue,thickness=2):
B:=seq(plottools[disk]([(R-r)*cos(2*Pi*k/N),(R-r)*sin(2*Pi*k/N)],r,
color=yellow),k=1..N):
C:=seq(plottools[disk]([(R-r)*cos(2*Pi*k/N)+r*cos(2*Pi*k/N-R*2*Pi*k/r/N),
(R-r)*sin(2*Pi*k/N)+r*sin(2*Pi*k/N-R*2*Pi*k/r/N)],r/15,color=red),k=1..N):
F:=seq(plot([(R-r)*cos(t)+r*cos(t-R*t/r),(R-r)*sin(t)+r*sin(t-R*t/r),
t=0..2*Pi*k/N],x=-R..R,y=-R..R,color=red,thickness=2),k=1..N):
for k from 1 to N do E[k]:=plots[display](A,C[k],B[k],F[k]); od:
plots[display]([seq(E[k],k=1..N)],insequence=true,scaling=constrained,
view=[-R-1..R+1,-R-1..R+1]);
[albumimg]192[/albumimg] [albumimg]193[/albumimg]
Russia ☭ forever, Viacheslav N. Mezentsev
1 users liked this post
ioan92 6/2/2013 2:53:00 AM
#162 Posted: 6/2/2013 1:57:14 AM
Good work uni
I've noted the "Export" button was added (maybe it was here but I missed it). This can be used to save the plot in the GIF format, animated or not, like the SMath's base plots.
I suppose copying the plots from one worksheet to another will be fixed as well as soon as the plot saving fix will work.
Regards,
Radovan

I've noted the "Export" button was added (maybe it was here but I missed it). This can be used to save the plot in the GIF format, animated or not, like the SMath's base plots.
I suppose copying the plots from one worksheet to another will be fixed as well as soon as the plot saving fix will work.
Regards,
Radovan
When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
#163 Posted: 6/2/2013 3:27:53 AM
Viacheslav,
Thank you for the new version of MapleWrapper plugin. This is really impressive to have so beautiful tool like your plugin in SMath Studio. Once again thank you heartily.
Regards,
Janusz
Thank you for the new version of MapleWrapper plugin. This is really impressive to have so beautiful tool like your plugin in SMath Studio. Once again thank you heartily.
Regards,
Janusz
#164 Posted: 6/2/2013 6:42:13 AM
Hello,
I know how to dissolve one differential equation of the any degree using MapleWrapper plugin. But how to dissolve the system of ODE using MapleWrapper, this unfortunately I do not know. Please for the help.
I tried in different ways to reach the result, however ineffective.
From above heartily thank you for your help.
Regards,
Janusz
I know how to dissolve one differential equation of the any degree using MapleWrapper plugin. But how to dissolve the system of ODE using MapleWrapper, this unfortunately I do not know. Please for the help.
I tried in different ways to reach the result, however ineffective.

From above heartily thank you for your help.
Regards,
Janusz
#165 Posted: 6/2/2013 3:38:15 PM
WroteHello,
I know how to dissolve one differential equation of the any degree using MapleWrapper plugin. But how to dissolve the system of ODE using MapleWrapper, this unfortunately I do not know. Please for the help.
I tried in different ways to reach the result, however ineffective.![]()
From above heartily thank you for your help.
Regards,
Janusz
I am not quite sure this was correctly solved using Maple
Regards,
Radovan
odesystem.sm (9 KiB) downloaded 94 time(s).
When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
#166 Posted: 6/3/2013 8:16:08 AM
Hello Radovan,
Thank you for these examples. I think that I know already where I made mistakes. Thank you also for your kind - already several times you helped me.
Regards,
Janusz
Thank you for these examples. I think that I know already where I made mistakes. Thank you also for your kind - already several times you helped me.
Regards,
Janusz
#167 Posted: 6/3/2013 9:31:47 AM
You are welcome Janusz
And do not hesitate to ask, as I always do
Regards,
Radovan

And do not hesitate to ask, as I always do
Regards,
Radovan
When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
#168 Posted: 6/4/2013 12:02:24 PM
Hello,
Make calculations in MapleWrapper must be record the tangent function as: "tan" what it is visible on the first picture. To closing of the file and his repeated opening SMath Studio changes the function tanges from the record: "tan" - required through MapleWrapper, on "tg", and in the this moment MapleWrapper cannot make calculations because it has implemented the tangent function as "tan" and not "tg" as in SMath Studio in the this moment - look the second picture. Well would be to standardize this mark of the tangent function in MapleWrapper and SMath Studio.
Regards,
Janusz
Before save:

After open:

Make calculations in MapleWrapper must be record the tangent function as: "tan" what it is visible on the first picture. To closing of the file and his repeated opening SMath Studio changes the function tanges from the record: "tan" - required through MapleWrapper, on "tg", and in the this moment MapleWrapper cannot make calculations because it has implemented the tangent function as "tan" and not "tg" as in SMath Studio in the this moment - look the second picture. Well would be to standardize this mark of the tangent function in MapleWrapper and SMath Studio.
Regards,
Janusz
Before save:
After open:
#169 Posted: 6/4/2013 12:16:39 PM
I think this is a bug (Smath Studio, not mine). The same works and for cot(). You can define the function tg():=tan() and it should work.
The names of the trigonometric functions depends on the settings of the program. I consider them.
The names of the trigonometric functions depends on the settings of the program. I consider them.
Russia ☭ forever, Viacheslav N. Mezentsev
#170 Posted: 6/4/2013 12:25:54 PM
Hello Uni,
Thank you for explanations and the council.
Regards,
Janusz
Thank you for explanations and the council.
Regards,
Janusz
#171 Posted: 6/4/2013 1:00:28 PM
#172 Posted: 6/4/2013 1:37:21 PM
Viacheslav,
This is very instructive and surprising
example. My congratulations! Thank you very much!
Regards,
Janusz
This is very instructive and surprising

Regards,
Janusz
#173 Posted: 6/6/2013 1:19:28 PM
Hello!
Please for the explanation why I receive two different results as this is visible on the example below:

Regards,
Janusz
Where is the error.sm (7 KiB) downloaded 85 time(s).
Please for the explanation why I receive two different results as this is visible on the example below:
Regards,
Janusz
Where is the error.sm (7 KiB) downloaded 85 time(s).
#174 Posted: 6/6/2013 1:45:19 PM
There is no error. This behavior depends on the relative positions of the expressions on the sheet. When you put the definition of x above of a function call, the variable x in the expression solver becomes zero.
[albumimg]199[/albumimg]
[albumimg]199[/albumimg]
Russia ☭ forever, Viacheslav N. Mezentsev
#175 Posted: 6/6/2013 1:54:16 PM
Hello Uni,
Thank you for the explanation. The first time I meet with such by chance.
Regards,
Janusz
Thank you for the explanation. The first time I meet with such by chance.
Regards,
Janusz
#176 Posted: 6/6/2013 2:20:16 PM
Uni,
I cannot obtain such result as you. Can I ask you for the source file of your results.
[albumimg]200[/albumimg]
Regards,
Janusz
I cannot obtain such result as you. Can I ask you for the source file of your results.
[albumimg]200[/albumimg]
Regards,
Janusz
#177 Posted: 6/6/2013 2:32:29 PM
I Installed MapleWrapper from the Online Gallery
It seems Maple is working fine, but, unfortunately, MaplePlot can not produce a plot for me. There are still "empty" plots there, in spite of inserting the plotting text inside them
.
I hope I did not do something wrong.
Regards,
Radovan
mvr5.txt (8 KiB) downloaded 69 time(s).

It seems Maple is working fine, but, unfortunately, MaplePlot can not produce a plot for me. There are still "empty" plots there, in spite of inserting the plotting text inside them

I hope I did not do something wrong.
Regards,
Radovan
mvr5.txt (8 KiB) downloaded 69 time(s).
When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
#178 Posted: 6/6/2013 2:46:01 PM
Not so fast
There's a bug. This is a test version for the new version SMath Studio. I'll combine Maple and MaplePlot regions.

Russia ☭ forever, Viacheslav N. Mezentsev
1 users liked this post
Radovan Omorjan 6/6/2013 3:36:00 PM
#179 Posted: 6/7/2013 11:32:03 AM
WroteThere is no error. This behavior depends on the relative positions of the expressions on the sheet. When you put the definition of x above of a function call, the variable x in the expression solver becomes zero.
[albumimg]199[/albumimg]
Hello,
Right now I noticed, that the power in the calculation of the value t (0) at the end of your sheet is positive. From here the conclusion: there is the error because the value t(0) have to be zero. The value x equal zero is given at the end because here I pass to numerical calculations.
If I am wrong please for the explanation.
Regards,
Janusz
#180 Posted: 6/7/2013 1:13:56 PM
When you are trying to calculate the last expression the maple() function takes the following expression (see mvr5\mvr5.txt):
07.06.2013 23:02:12 [->] solve({(0=(77/10000*ln({((77/10000+772893421/100000000000000*t*715*cos({(Pi/4)}))/77/10000)}))/772893421/100000000000000)},t)
07.06.2013 23:02:12 [->] C:\Temp\tmp1B5E.tmp:
interface(quiet=true);
with(linalg):with(inttrans):with(plots):
writeto("C:\\Temp\\tmp1B5F.tmp"):
smath_line := proc() local i: for i from 1 to nargs - 2 do args[i]; od: end:
smath_sum := proc() if nargs = 1 then sum( args[1] ); elif nargs = 2 then sum( args[1], args[2] ); elif nargs = 4 then sum( args[1], args[2] = args[3] .. args[4] ); fi: end:
smath_product:= proc() if nargs = 1 then product( args[1] ); elif nargs = 2 then product( args[1], args[2] ); elif nargs = 4 then product( args[1], args[2] = args[3] .. args[4] ); fi: end:
smath_int := proc() if nargs = 2 then int( args[1], args[2] ); elif nargs = 4 then int( args[1], args[2] = args[3] .. args[4] ); fi: end:
smath_diff := proc() if nargs = 2 then diff( args[1], args[2] ); elif nargs = 3 then diff( args[1], args[2] $ args[3] ); fi: end:
smath_sys := proc() { args[i] $ i = 1 .. nargs - 2 }; end:
smath_el := proc() args[1][ args[2] ]; end:
smath_mat := proc()
local i, j, out:
out := [ args[j] $ j = 1 .. args[ nargs ] ]:
for i from 2 to args[ nargs - 1 ] do
out := out, [ args[j] $ j = ( i - 1 ) * args[ nargs ] + 1 .. ( i - 1 ) * args[ nargs ] + args[ nargs ] ]:
od:
convert( [ out ], array );
end:
smath_submatrix := proc() submatrix( args[1], args[2] .. args[3], args[4] .. args[5] ); end:
ans := \
solve(((0=(77/10000*ln((((77/10000+772893421/100000000000000*t*715*cos\
(((Pi/4))))/77/10000))))/772893421/100000000000000)),t):
if ( whattype( ans ) = `exprseq` ) then
convert( convert( cat( `mat(`, substring( convert( [ans], string ), 2..-2 ), `,`, nops( [ans] ), `,1)` ), string ), symbol );
elif ( whattype( ans ) = `set` ) then
convert( convert( cat(`mat(`,substring(convert(map2(op,2,[ans[i]$i=1..nops(ans)]),string),2..-2),`,`,nops(ans),`,1)`), string ), symbol );
elif ( whattype( ans ) = `symbol` ) then
convert( convert( eval( ans ), string ), symbol );
elif ( whattype( ans ) = `series` ) then
convert( convert( ans, polynom) , symbol );
elif ( whattype( ans ) = `string` ) then
convert( ans, symbol );
else
convert( convert( ans, string ), symbol ); fi;
quit:
07.06.2013 23:02:12 [<-] C:\Temp\tmp1B5F.tmp:
1399999986000000000/10047614473*2^(1/2)
07.06.2013 23:02:12 [<-] 1399999986000000000/10047614473*2^(1/2)
As you can see: solve({(0=, but you expected solve({(x=. That's the difference. The solve() function solves another equation.
07.06.2013 23:02:12 [->] solve({(0=(77/10000*ln({((77/10000+772893421/100000000000000*t*715*cos({(Pi/4)}))/77/10000)}))/772893421/100000000000000)},t)
07.06.2013 23:02:12 [->] C:\Temp\tmp1B5E.tmp:
interface(quiet=true);
with(linalg):with(inttrans):with(plots):
writeto("C:\\Temp\\tmp1B5F.tmp"):
smath_line := proc() local i: for i from 1 to nargs - 2 do args[i]; od: end:
smath_sum := proc() if nargs = 1 then sum( args[1] ); elif nargs = 2 then sum( args[1], args[2] ); elif nargs = 4 then sum( args[1], args[2] = args[3] .. args[4] ); fi: end:
smath_product:= proc() if nargs = 1 then product( args[1] ); elif nargs = 2 then product( args[1], args[2] ); elif nargs = 4 then product( args[1], args[2] = args[3] .. args[4] ); fi: end:
smath_int := proc() if nargs = 2 then int( args[1], args[2] ); elif nargs = 4 then int( args[1], args[2] = args[3] .. args[4] ); fi: end:
smath_diff := proc() if nargs = 2 then diff( args[1], args[2] ); elif nargs = 3 then diff( args[1], args[2] $ args[3] ); fi: end:
smath_sys := proc() { args[i] $ i = 1 .. nargs - 2 }; end:
smath_el := proc() args[1][ args[2] ]; end:
smath_mat := proc()
local i, j, out:
out := [ args[j] $ j = 1 .. args[ nargs ] ]:
for i from 2 to args[ nargs - 1 ] do
out := out, [ args[j] $ j = ( i - 1 ) * args[ nargs ] + 1 .. ( i - 1 ) * args[ nargs ] + args[ nargs ] ]:
od:
convert( [ out ], array );
end:
smath_submatrix := proc() submatrix( args[1], args[2] .. args[3], args[4] .. args[5] ); end:
ans := \
solve(((0=(77/10000*ln((((77/10000+772893421/100000000000000*t*715*cos\
(((Pi/4))))/77/10000))))/772893421/100000000000000)),t):
if ( whattype( ans ) = `exprseq` ) then
convert( convert( cat( `mat(`, substring( convert( [ans], string ), 2..-2 ), `,`, nops( [ans] ), `,1)` ), string ), symbol );
elif ( whattype( ans ) = `set` ) then
convert( convert( cat(`mat(`,substring(convert(map2(op,2,[ans[i]$i=1..nops(ans)]),string),2..-2),`,`,nops(ans),`,1)`), string ), symbol );
elif ( whattype( ans ) = `symbol` ) then
convert( convert( eval( ans ), string ), symbol );
elif ( whattype( ans ) = `series` ) then
convert( convert( ans, polynom) , symbol );
elif ( whattype( ans ) = `string` ) then
convert( ans, symbol );
else
convert( convert( ans, string ), symbol ); fi;
quit:
07.06.2013 23:02:12 [<-] C:\Temp\tmp1B5F.tmp:
1399999986000000000/10047614473*2^(1/2)
07.06.2013 23:02:12 [<-] 1399999986000000000/10047614473*2^(1/2)
As you can see: solve({(0=, but you expected solve({(x=. That's the difference. The solve() function solves another equation.
Russia ☭ forever, Viacheslav N. Mezentsev
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