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UseUnit...

Answered: acer 32617

October 24 2018

1 2

Since Maple 15 it is even easier to set the default unit for a particular dimension with the UseUnit command. I mean easier than having to use the commands AddSystem and UseSystem as you did above.

This allows other scales of power to be simplified to your desired kWh/day.

You can utilize it with or without loading Units:-Standard, depending on whether you want arithmetic with units to resolve/combine automatically. Or in recent versions you can utilize it alongside Units:-Simple, which does that automatic combining of units while also allow mixed arithmetic of quantities with units attached and unknown quantities (eg. names) without units specified.

>

restart;

>	kernelopts(version);

>	Units:-UseUnit(kWh/day):

>	expr1 := 4.9Unit(kW)3.5*Unit(h/day);

>	combine(expr1, units); # no change, as desired

>	expr2 := 1700.1*Unit(W);

>	combine(expr2, units);

>	simplify(expr2);

>

restart;

>	Units:-UseUnit(kWh/day):

>	with(Units:-Standard):

>	4.9Unit(kW)3.5*Unit(h/day);

>	simplify(1700.1*Unit(W));

>	1700.1Unit(W)3.4*Unit(days/week);

>

restart;

>	Units:-UseUnit(kWh/day):

>	with(Units:-Simple):

>	4.9Unit(kW)3.5*Unit(h/day) + x;

>	simplify(1700.1*Unit(W) - u);

>	1700.1Unit(W)3.4Unit(days/week) + 40.5k;

>

Download useunit.mw

There are also facilities for right-click units re-formatting in the Maple 2018 GUI. You can also use that (or convert(...,units,W) ) to force display in Watts alone.

Physics:-diff...

Answered: acer 32617

October 23 2018

1 6

@primogen Have you tried,

Physics:-diff~(SimplifiedMassMatrixDot, theta[2](t));

a_ac.mw

I toggled this Question to be marked as "Maple 2017", since that's the release in which your attachment was last saved. (You had it as "Maple 17" which is four major releases earlier.)

2D Output only...

Answered: acer 32617

October 23 2018

1 0

I don't know of any easy way to handle 2D Input of units (ie. typeset via command-completion, or from the Units palette).

The following affects 2D Output. (I doubt it will work alongside right-click unit-formatting.)

>

restart;

>	kernelopts(version);

>

>	Unit(88kgm/s^2) + Unit(g)Unit(-3cm/s^2);

>

ChangeUnitsColor:=proc(c, {bold::truefalse:=false})
  global `print/Unit`;
  local hexstr;
  uses ColorTools;
  if c = ':-default' then
    `print/Unit`:='`print/Unit`';
    return NULL;
  end if;
  hexstr:=RGB24ToHex(RGBToRGB24([ColorTools:-Color(c)[]]));
  `print/Unit`:=subs(__dummy=hexstr,
      proc(x)
      local r;
      uses T=Typesetting;
      if interface(':-prettyprint')<2 then
        return Units:-Unit(args);
      end if;
      r:=subsindets(T:-Typeset(x),
                    ':-specfunc'({T:-mrow,T:-mi,T:-mo,
                                  T:-mfrac,T:-msup,T:-msqrt}),
                    u->op(0,u)(op(u),
                               "mathcolor"=__dummy));
      r:=subsindets(r,specfunc({T:-mi,T:-mo}),
                    u->T:-mtext(op(u)));
      if bold=true then
        r:=T:-mstyle(r, 'italic'="false", ':-fontweight'="bold");
      end if;
      return r;
    end proc);
  NULL;
end proc:

>

>	ChangeUnitsColor("Red");

>	Unit(kg^(1/2));

>	Unit(s/m)+Unit(day/cm);

>	simplify(Unit(s/m)+Unit(day/cm));

>	ChangeUnitsColor("Green");

>	sin(x)Unit(8.8kgm/s^2) + Unit(g)Unit(-3*cm/s^2);

>	combine(%, units);

>	ChangeUnitsColor("Blue", bold);

>	sin(x)Unit(8.8kgm/s^2) + Unit(-3g*cm/s^2);

8.8*sin(x)*Units:-Unit(kg*m/s^2)-3*Units:-Unit(g*cm/s^2)

>

>	ChangeUnitsColor(default);

>	sin(x)Unit(8.8kgm/s^2) + Unit(g)Unit(-3*cm/s^2);

>

Download unitcolorbold.mw

some results...

Answered: acer 32617

October 22 2018

0 0

>

restart;

>	g := x -> (2*x-7)^('-3');

>	new := InertForm:-MakeInert(g(x)):

>	InertForm:-Display(new,inert=false);

>

g(6);

>	other := subs(x=6, new):

>	InertForm:-Display(other, inert=false);

>	value(other);

>	map[2](op,2,indets(g(x), `^`));

>	-degree(denom(g(x)),x);

>

Download inertanother.mw

some results...

Answered: acer 32617

October 22 2018

0 2

>

restart;

>	kernelopts(version);

>	assume(x>0);

>	expr := sqrt(x^3*x^(3/4));

>	new := combine(expr);

>	map[2](op,2,indets(new,identical(x)^anything));

>

restart;

>	expr := surd(a'surd'(aa^b,2),4);

>	inertexpr := InertForm:-MakeInert(eval(expr,1)):

>	new := subs([a=2,b=6,c=4], inertexpr):

>	ans := InertForm:-Display(new, inert=false);

>	InertForm:-Value(new);

>

Download inertsurd.mw

multiple assignment...

Answered: acer 32617

October 22 2018

0 0

The multiple assignment functionality was added in Maple V R5 which was released in 1997.

Array plot?...

Answered: acer 32617

October 19 2018

1 1

Have you tried,

display(Array([ display(A,B), C ]));

More importantly, Shouldn't you call it like,

Explore( P(a), parameters=[a=-1.0..1.0] );

so that it explores a function call to P?

Embedded Components...

Answered: acer 32617

October 19 2018

0 0

Yes, you should be to accomplish this using Embedded Components, as long as the data exists before the plotting begins.

If you're hoping for an asynchronous process that sits there waiting for newly computed data points to be added to the file then the task is much more complicated (if possible at all).

Do you have a sample of data? What kind of plot do you want?

worksheet...

Answered: acer 32617

October 18 2018

0 0

You can map the diff command over the Matrix.

step1calshelper_ac.mw

I also show various simplifications (and their effects on the size of the Matrix entries).

Matrix...

Answered: acer 32617

October 18 2018

0 1

Make a Matrix with the two lists as its columns (ie. column Vectors).

A := [[0, 1, 2, 3, 4, 5], [0, 2, 4, 6, 8, 10]]:
M:=<<A[1]>|<A[2]>>:
ExportMatrix(test, M, delimiter=" "):

Alternatively, create the Matrix with the lists as the rows, and export its transpose.

A := [[0, 1, 2, 3, 4, 5], [0, 2, 4, 6, 8, 10]]:
M:=Matrix(A):
ExportMatrix(test, M^%T, delimiter=" "):

Maple...

Answered: acer 32617

October 16 2018

1 0

It cannot be done straight from Maple, AFAIK.

It would be interesting if someone proved me wrong by showing a way using the Maple's HTTP or URL (or lower level via Sockets). Its not clear to me how login or authentification might work.

It'd be trickier still, since uploads to Mapleprimes are attachments to posts. It might be more effort to upload without a post (and then somehow post separately and attach the prior raw upload) or to effect both directly from Maple.

Upload and insertion of a link to the worksheet, or inlining of the worksheet, is available from within Mapleprimes using the green up-arrow that appears in the menubar of the Question/Reply/Post editor.

Upload to the Maplecloud is possible, directly from Maple. But I'm not aware that Mapleprimes and the Maplecloud have any functional interchange.

several ways...

Answered: acer 32617

October 16 2018

0 1

The easiest way is to put both subpackages within a single parent package.

If you really want them distinct then you can utilize an abbreviation scheme. Here are two choices for that:

1) Utilize the $define preprocessor directive in the source. (I prefer to load all my packages from source code stored in plaintext files outside of any worksheet.) For example,

$define OPFCN OriginalPackage:-Function

# alternatively
$define OP OriginalPackage
$define FCN Function

The second of those would be utilized by accessing OP:-FCN in the subsequent code.

At the end of the source file you can utilize the corresponding $undef directives.

2) Utilize the uses syntax at the start of the source for each procedure in the dependent (2nd) package. For example,

NewFunction := proc(x)
  local blah,blech;
  uses OP=OriginalPackage,
       OPFCN=OriginalPackage:-Function;

  blah := OP:-OtherFunction(x);
  blech := OPFCN(blah*x);
end proc;

collect ?...

Answered: acer 32617

October 12 2018

0 0

If the whole equation is assigned to the name eqn , then how about,

collect( expand(lhs(eqn)), Rm, simplify ) = rhs(eqn);

some ideas...

Answered: acer 32617

October 12 2018

2 6

Here are some ideas for reducing the size of the over expression, and one example of substituting names for common subexpressions.

>

restart;

>

A:=Matrix([[phi,conjugate(psi),chi,conjugate(rho)],
          [psi,-conjugate(phi),rho,-conjugate(chi)],
          [lambda1*phi,conjugate(lambda1)*conjugate(psi),
           lambda2*chi,conjugate(lambda2)*conjugate(rho)],
          [lambda1*psi,-conjugate(lambda1)*conjugate(phi),
           lambda2*rho,-conjugate(lambda2)*conjugate(chi)]]);

>	d := LinearAlgebra:-Determinant(A):

>	d; length(%);

>	simplify(d,size); length(%);

>	collect(d,[rho,chi],u->simplify(u,size)); length(%);

>	collect(d,[psi,phi],u->simplify(u,size)); length(%);

>	collect(d,[lambda1,lambda2],u->map(factor,simplify(u,size))); length(%);

>

R1:=abs(lambda1)^2+abs(lambda2)^2-conjugate(lambda2)*lambda1-conjugate(lambda1)*lambda2=K1:
R2:=abs(lambda1)^2+abs(lambda2)^2-conjugate(lambda2)*conjugate(lambda1)-lambda1*lambda2=K2:
R3:=conjugate(psi)*phi*rho*conjugate(chi)=K3:
R4:=chi*conjugate(phi)*conjugate(rho)*psi=conjugate(K3):
temp := simplify(collect(d,[rho,chi],u->simplify(u,size))):
new := simplify(subs([R1,R2,R3,R4],temp),size);
(rhs=lhs)(R1);
(rhs=lhs)(R2);
(rhs=lhs)(R3);

>	# check subs([(rhs=lhs)(R1),(rhs=lhs)(R2),(rhs=lhs)(R3)], new): combine(simplify(eval(simplify((% - d)), [lambda1=Re(lambda1)+IIm(lambda1), lambda2=Re(lambda2)+IIm(lambda2)])));

>

Download some_simp.mw

inner integral...

Answered: acer 32617

October 11 2018

1 4

In my Maple 2018.1 the integral of dex for t=0..phi2 can be done symbolically, under assumptions consisting of the bounds of the outer variables' ranges of integration. This leads to a triple integral that can be done quickly and accurately, numerically, without need to specify a particular method.

>

restart;

>	with(LinearAlgebra):

>	r1 := Vector([0, 0, 1]):

>	r2 := Vector([sin(theta1), 0, cos(theta1)]):

>	r3 := Vector([sin(theta2)cos(phi2), sin(theta2)sin(phi2), cos(theta2)]):

>	M := Matrix([r1, r2, r3]);

Matrix(3, 3, {(1, 1) = 0, (1, 2) = sin(theta1), (1, 3) = sin(theta2)*cos(phi2), (2, 1) = 0, (2, 2) = 0, (2, 3) = sin(theta2)*sin(phi2), (3, 1) = 1, (3, 2) = cos(theta1), (3, 3) = cos(theta2)})

>	ex := simplify(Determinant(M)/(1+DotProduct(r1,r2)+DotProduct(r1,r3)+DotProduct(r2,r3))) assuming theta1 > 0, theta2 > 0, phi2 > 0;

>	dex := eval(simplify(diff(arctan(ex), phi2)), phi2 = t);

>	Q := simplify(int(dex, t = 0 .. phi2)) assuming theta1 > 0, theta1 < Pi, theta2 > 0, theta2 < Pi, phi2 > 0, phi2<Pi;

(1/2)*phi2-arctan((cos(theta2)*cos(theta1)-sin(theta2)*sin(theta1)+1)*sin((1/2)*phi2)/(cos((1/2)*phi2)*abs(cos(theta2)+cos(theta1))))*signum(cos(theta2)+cos(theta1))

>	Tother := 2Int( 2Q/(4Pi) 2Pisin(theta1)sin(theta2)/(4Pi4Pi), [phi2 = 0 .. Pi, theta2 = 0 .. Pi, theta1 = 0 .. Pi] );

2*(Int((1/16)*((1/2)*phi2-arctan((cos(theta2)*cos(theta1)-sin(theta2)*sin(theta1)+1)*sin((1/2)*phi2)/(cos((1/2)*phi2)*abs(cos(theta2)+cos(theta1))))*signum(cos(theta2)+cos(theta1)))*sin(theta1)*sin(theta2)/Pi^2, [phi2 = 0 .. Pi, theta2 = 0 .. Pi, theta1 = 0 .. Pi]))

>	alt := simplify(combine(Tother));

Int(-(1/32)*(cos(-theta2+theta1)-cos(theta2+theta1))*(2*arctan((1/2)*(sin((1/2)*phi2+theta2+theta1)+sin((1/2)*phi2-theta2-theta1)+2*sin((1/2)*phi2))/(abs(cos(theta2)+cos(theta1))*cos((1/2)*phi2)))*signum(cos(theta2)+cos(theta1))-phi2)/Pi^2, [phi2 = 0 .. Pi, theta2 = 0 .. Pi, theta1 = 0 .. Pi])

>	evalf(alt); # no special method specified

>	T := 2Int( 2Int(dex, t = 0 .. phi2)/(4Pi) 2Pisin(theta1)sin(theta2)/(4Pi4Pi), [phi2 = 0 .. Pi, theta2 = 0 .. Pi, theta1 = 0 .. Pi] );

2*(Int((1/16)*(Int((1/2)*sin(theta1)*((cos(theta2)+1)*(cos(theta1)+1)*cos(t)+sin(theta2)*sin(theta1))*sin(theta2)/((cos(theta2)+1)*(cos(theta1)+1)*(sin(theta1)*sin(theta2)*cos(t)+cos(theta2)*cos(theta1)+1)), t = 0 .. phi2))*sin(theta1)*sin(theta2)/Pi^2, [phi2 = 0 .. Pi, theta2 = 0 .. Pi, theta1 = 0 .. Pi]))

>	# vv's idea new := IntegrationTools:-Change(T, t=sphi2, [s]): new := simplify(IntegrationTools:-CollapseNested(frontend(combine,[%],[{`+`,``,specfunc(Int)},{}])));

Int((1/16)*sin(theta2)^2*phi2*((cos(theta2)+1)*(cos(theta1)+1)*cos(s*phi2)+sin(theta2)*sin(theta1))*sin(theta1)^2/((cos(theta2)+1)*(cos(theta1)+1)*Pi^2*(sin(theta1)*sin(theta2)*cos(s*phi2)+cos(theta2)*cos(theta1)+1)), [s = 0 .. 1, phi2 = 0 .. Pi, theta2 = 0 .. Pi, theta1 = 0 .. Pi])

>	subsindets(new,specfunc(Int),u->Int(op(u),method = _CubaCuhre, epsilon = 1e-5)): evalf(%);

>

Download multi_int.mw

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These are answers submitted by acer

UseUnit...

Physics:-diff...

2D Output only...

some results...

some results...

multiple assignment...

Array plot?...

Embedded Components...

worksheet...

Matrix...

Maple...

several ways...

collect ?...

some ideas...

inner integral...

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