Multiple equalities in a Mathcad Equation

[tubar]

Why Mathcad do not allow equalities like:

a:=(x+y)^2:=x^2+y^2+2*x*y

in witch to consider finally as a equality between first and last term? so being a:=x^2+y^2+2*x*y

Mathcad dont allow to insert a second equal sign in a given equation where to expose succesively the intermediary forms of a given identity.

[jeanGiraud]

What you attempted has no mathematical meaning, then no use.

The purpose of writing an equality is to solve for some of the variables ,

like in the qs examples [if you want to produce something].

Some functions have more than the simple book style.

Here is the longest found in the Mathcad collab [yellow].

Then, there is/are the equal forms that do not numerically

execute the same way. Those cases are hard to find, they

will generally arrive from the designer.

jmG

[IRstuff]

Unclear what you are trying to do. If you are using the symbolic processor, it already understands the second equivalence.

TTFN

[mzeftel]

To get what you want, a:=(x+y)^2:=x^2+y^2+2*x*y.

Type in (x +y)^2 then apply symbolic expand from the Symbolics palette.

Mona

[tubar]

nope, is not necessary to use mathcad processor for simple cases.

Is a problem of flexibility for Mathcad, that's all. My proposal is not in any contradiction with anithing. It respect all mathematical rule. Mathcad instead is not flexible in this option.

My proposal is to make somehow Mathcad to edit equations just like in our notebook, is the most natural way.

I give an example.

a:=2

b:=a+7=9

The upper example is accepted by mathcad.

Then why Mathcad cannot accept this:

y:=(x+1)^2:=x^2+2*x+1

is like to give a small detail for the path of equations exposed.

For mathcad processor the routine is simple:

if find a second ":=" in equation, then keep the last member of equality to be equal with the first

Why should I write 2 times a equation inside mathcad to obtain a result.

Other Example:

t:=a+3

z:=t^2

z:=a^2+6*a+9

For this simple case i dont need to use mathcad processor and hardware resources, i just have to be able to write directly as below:

t:=a+3

z:=t^2:=a^2+6*a+9

Mathcad will understand last equation as being z:=a^2+6*a+9 (second equal take all task of the previous equal, so remain kept first and last terms, intermediary are skip)

Why cannot be implemented this? Is a problem of flexibility.

This rule is not in contradiction with any mathematical rule, and also not contradict even with just Mathcad source code.

For complicated cases indeed is necessary to use the command expand. But for simple cases is not necessary, when just I have in mind the result and i can expose it to detail equation in a cognitive way.

So, in my opinion Mathcad code have to be upgraded for some cases where is problem of flexibility.

[RichardJ]

tudor baracu wrote:

nope, is not necessary to use mathcad processor for simple cases.

Is a problem of flexibility for Mathcad, that's all. My proposal is not in any contradiction with anithing. It respect all mathematical rule. Mathcad instead is not flexible in this option.

My proposal is to make somehow Mathcad to edit equations just like in our notebook, is the most natural way.

I give an example.

a:=2

b:=a+7=9

The upper example is accepted by mathcad.

Then why Mathcad cannot accept this:

y:=(x+1)^2:=x^2+2*x+1

is like to give a small detail for the path of equations exposed.

In te first example one operator is an assignment, the second is an evaluation. That is fine. In the second example the second assignment attpts to assign an expression to an expression, which cannot be done. For good reason.

if find a second ":=" in equation, then keep the last member of equality to be equal with the first

That woud permit me to write

y:=(x+1)^2:=x^3+47x+908

Which is obviously garbage, so it's not allowed.

Why should I write 2 times a equation inside mathcad to obtain a result.

You don't have to write it twice. One pf the things you are trying to do is a symbolic math operation: i.e. change the form of an expression. So you need to use the symbolic processor to do it.

Other Example:

t:=a+3

z:=t^2

z:=a^2+6*a+9

For this simple case i dont need to use mathcad processor and hardware resources, i just have to be able to write directly as below:

t:=a+3

z:=t^2:=a^2+6*a+9

Mathcad will understand last equation as being z:=a^2+6*a+9 (second equal take all task of the previous equal, so remain kept first and last terms, intermediary are skip)

You can do that, see the attached. What you want to do is not allowed because it leaves you to decide the symbolic relationship between the two experssions. Quite possibly incorrectly

Suppose I wrote

z:=sqrt(x^2):=x

Perhaps there is a problem there?

This rule is not in contradiction with any mathematical rule

It is if you get the symbolic math wrong

and also not contradict even with just Mathcad source code.

It is completely in conflict with it.

[tubar]

In actual stage of Mathcad indeed are contradictions because it doesnt allow to me to write a second equality. OK

But inside a source code of Mathcad can be implemented this:

if found second equality sign, than process equality between first and last

For z:=(a+1)^2+1:=a^2+2*a+1+1:=a^2+2*a+2

Mathcad will process z:=a^2+2*a+2 Equality between first and last - principle of black box (in a black box no matter intermediary, it matter only input and output)

In a notebook u use frequently equations with many equals inside a equation, aiming to get an acceptable form, isnt it?

So when you write:

z:=(a+1)^2+1:=a^2+2*a+1+1:=a^2+2*a+2 you want in fact in the last to exprimate that z:=a^2+2*a+2 ok?

Then in notebook instead to write like this:

z:=(a+1)^2+1

z:=a^2+2*a+1+1

z:=a^2+2*a+2

You write instead this: z:=(a+1)^2+1:=a^2+2*a+1+1:=a^2+2*a+2 aiming in fact z:=a^2+2*a+2

Then MAthcad have to process in a same manner. If meet a second equal in a equation will take as equality between first and last

Will be a good generalisation of aproach if Mathcad follow my advice

[RichardJ]

tudor baracu wrote:

In actual stage of Mathcad indeed are contradictions because it doesnt allow to me to write a second equality. OK

It is not a second equality. It is a second assignment, and assigning one expression to another is meaningless. Therefore it's not allowed

z:=(a+1)^2+1:=a^2+2*a+1+1:=a^2+2*a+2 you want in fact in the last to exprimate that z:=a^2+2*a+2 ok?

Not OK if you get the symbolic math wrong, no. Mathcad has a symbolic processor that allows you to do what you want without the possibility of making a typographical error. So why do you want to do the symbolic math by hand?

You write instead this: z:=(a+1)^2+1:=a^2+2*a+1+1:=a^2+2*a+2 aiming in fact z:=a^2+2*a+2

Then MAthcad have to process in a same manner.

It does process in that manner, as I have shown you in several examples. What it does not allow is for you to do the processing yourslf and manually insert an expression that may not even be correct.

[tubar]

Yes, indeed, may even not be correct. Good observation. But give to the user possibility to choose. A mistake could be inserted from many other ways, why my case would had been a exception.

But is a shortcut that user can use and profit from it. Mistakes comes from anywhere.

Yes, my request is simple. Mathcad to allow more equal signs. Scientifically is correct to have more equalities, and Mathcad try to be closed to science. Then have to be closed as possible with sciences. User have to be cautious anyhow to not do mistakes.

I apreciate that we could have direct talks about mathcad tools.

[RichardJ]

Those are not equalities, they are assignments. The second assignment would attempt to assign one expression to another expression. That is not allowed, because it is meaningless.

Mathcad has two processors, numeric and symbolic, that are largely separate. It has assignment, local assignment, numeric evaluation, symbolic evaluation, and equality operators.

Here's a very brief tutorial.

[tubar]

Indeed, asignments. Then Mathcad need a bit of more flexibility about this.

If meet 2 asignments in a equation, then have to take as being assignment between first and last term, intermediary being skipped. Why cannot be possible this? Is a generalisation. Who want to use the way I propose, he can do with a lot of shortcuts that will obtain in shorting the work, and who dont want, can use the classical way that Mathcad did by now.

My proposal not contradict with Mathcad approach that did by now. My proposal generalize the existing aproach.

Is the principle of Black Box: take in consideration input and output - so if more than one assignment in a equation, then keep first and last term (equality between first and last term)

Please, open your mind, dont be only programmer

[RichardJ]

Is the principle of Black Box: take in consideration input and output - so if more than one assignment in a equation, then keep first and last term (equality between first and last term)

And allow someone to insert whatever they want in the middle term, no matter if it's completely wrong and misleading? Sorry, but I don't think that's a good idea at all

Please, open your mind, dont be only programmer

Who said I'm a programmer? I'm a physicist.

[tubar]

Ok, Ok physicist. Than i am surprised you cannot understand what i want to say.

In a copybook/notebook you can assign many equals aiming a final form of left member to be equal to an expression in a equation, and in MAthcad you cannot. How you interpret this?

We have us to update to Mathcad? Or Mathcad to update to our human science ?

And what i propose is not in contradiction with anything. Anything. Just is a way of flexibility for Mathcad. Who want will use this shortcut I propose if is smart enough, who dont will not use continuing in a classic manner.

My proposal not change anything in Mathcad, just would make Mathcad more friendly when interact with user. That's all

[RichardJ]

tudor baracu wrote:

Ok, Ok physicist. Than i am surprised you cannot understand what i want to say.

I understand what you want. I have shown you how to get it. What I do not understand is what is unacceptable about what Mathcad can do.

In a copybook/notebook you can assign many equals aiming a final form of left member to be equal to an expression in a equation, and in MAthcad you cannot. How you interpret this?

Because in a notebook you can write whatever you want, regardless of whether or not it's correct. If you want to do all the math by hand and then write an expression that may or may not be correct why bother with Mathcad? I can do this in Word:

x=412

y:=(x+2)^3+4:=x^2+47=3

but it's complete garbage. The point of Mathcad is that it does the math for you, so that what I actually get is

y:=(x+2)^3+4:=(412+2)^3=70957948

which is correct.

[tubar]

Yeesss ! You are closer in what I want to say. For simple example that you gave indeed is a garbage. But if I have a worksheet in Mathcad and somebody read equations written in Mathcad for him will be more more easier to understand what is there !!!! more easier. And also is easy for the customer that write equations in Mathcad to structure in his mind the paths of how to put equations, to order well in mind equations, etc.

Shortly: I dont want to write initially equations on a paper then to translate them for mathcad.

I just want to be able to write directly equations in Mathcad and to be allowed to apply all rules that exist in science without to be limitated

[RichardJ]

Shortly: I dont want to write initially equations on a paper then to translate them for mathcad.

We agree about that. But what I am saying is that if you have Mathcad and are doing symbolic math, you should be using Mathcad to do it. It is much less likely to make a mistake than you are. It's not impossible it will make a mistake, because there are some bugs, but it is much less likely. So it is always a good idea ti run some example numbers through the expressions to make sure they are correct.

What you seem to want to do is not only to do the symbolic math by hand, but then also to be able to insert it into a Mathcad sheet in such a way that it looks like Mathcad did the symbolic calculations. Sorry, but I will never agree that should be permitted. If you wish to do the math by hand and then insert the results in a Mathcad worksheet then that is already permitted, just not in a way that is so misleading to someone else reading the worksheet or a printout of it.

I think we will have to agree to disagree on this one.

[tubar]

OK, that it is. At least I am satisfied that you understood well my proposal, with all my argues I insisted to present.

I repeat, is a good choise from you (Mathcad) to have direct talks with testers. Is a verry verry good way.

[RichardJ]

I repeat, is a good choise from you (Mathcad) to have direct talks with testers. Is a verry verry good way.

I don't work for PTC. I'm just a user, like you.

I agree it's good to discuss such proposals though. It's the best way to find their good points and bad points.

[tubar]

Yes, if somebody will use this method for sure is a smart guy that make easier his life

Mathcad cannot prevent user from something, because Mathcad being worried that user is a mistaker

If in reallity, in sciences in a equation manuscript are accepted more equals aiming that left term to be equal with a final obtained term from right side, why Mathcad is in contradiction with this rule of Sciences ? Mathcad want to be as closed of possible with rules from sciences

And what I propose is a generalisation that user can use it or not. Just give to user more paths of approaches.

Also help for someone that read solved equation, to see the way of how equations are exposed there.

Mathcad not have to be just a crowd of equations put by somebody there to be solved. Not, MAthcad have to be as closed as possible with methods of solving and also with methods of exposing equations in sciences.

What i propose is just a insertion of a check inside Mathcad source code like this: if found in current equation a second equal by definition, than consider that the term from left side is equal with the term from right side of the last equal. Thats all.

[RichardJ]

If in reallity, in sciences in a equation manuscript are accepted more equals aiming that left term to be equal with a final obtained term from right side, why Mathcad is in contradiction with this rule of Sciences ? Mathcad want to be as closed of possible with rules from sciences

I have shown how to do it. You stil have not told me what is wrong with the approach I have shown.

Also help for someone that read solved equation, to see the way of how equations are exposed there.

Do you mean the intermediate results from the symbolic processor? The symbolic processor does not do things the same way you do, so they would not be useful.

What i propose is just a insertion of a check inside Mathcad source code like this: if found in current equation a second equal by definition, than consider that the term from left side is equal with the term from right side of the last equal. Thats all.

I know what you are proposing. And I am saying that allowing someone to do the symbolic math by hand and then insert whatever expression they come up with, regardless of whether ot not it's correct, in a Mathcad expression is a bad idea. The point of Mathcad is that it does the math for you, so if you want to do it by hand and then write the type of expression you are proposing, even if it's not correct, then Mathcad is the wrong tool.

[tubar]

No ! No! why you say this ???? Is applying just a principle from Cybernetics: of black box . Input and output is valid, not what is inside of the black box.

And way that i propose is a alternative. This alternative dont replace existing. Who want to insert a second equal can insert, let him free, who won't then use methods by now.

Believe me, if you insert this idea, will be a small progress, but a verry positive one to make Mathcad more flexible with user.

Mathcad havent to be more carefull about something than user himself. Even user do something wrong in intermediary parts of equation with many equals, he will be able to check rapidly some errors.

But if he insert direcly in first equal a mistake, then is not a error ? is just a error hardly to find sometimes.

So in my proposal if come a error, will be rapidly identified, if it affect the results. If it dont affect results because is skipped (being in intermediary equals) than is still OK. Mathcad did the job of obtaining results.

[RichardJ]

tudor baracu wrote:

No ! No! why you say this ???? Is applying just a principle from Cybernetics: of black box . Input and output is valid, not what is inside of the black box.

In your proposal the box is not black at all. You are showing what is inside it.

So in my proposal if come a error, will be rapidly identified, if it affect the results. If it dont affect results because is skipped (being in intermediary equals) than is still OK. Mathcad did the job of obtaining results.

I completely disasgree that it's OK. The fact that it's written that way in a Mathcad worksheet implies to someone looking at the sheet or a printout of it that Mathcad did the calculation, or at least verified it, and that therefore it's highly likely to be correct. That is not the case though.

[tubar]

Anyway, I used all my experience in sciences to give a important feedback. If in present not appear to be strong my argues, i hope in the future to be.

I have a lot of experience in sciences, believe me. Engineering, physics, mathematics, and I did not just wrote equations to obtain results. This can do also monkeys . I just did researches in the boundary zones of sciences for some of them still are not books written in speciffic domains. Even I am teenager this cannot describe my skills :). I know all difficulties that happen when interact with Mathcad.

What I have to say is anytime when a interface is more flexible is more risk to appear errors, indeed. And what are solutions in general, to impose restrictions for some fearings, or just to let creation to manifest in a wider path and to avoid formal/arbitrary constraints (given by present, or mentallities, etc) ?

[RichardJ]

What I have to say is anytime when a interface is more flexible is more risk to appear errors, indeed. And what are solutions in general, to impose restrictions for some fearings, or just to let creation to manifest in a wider path and to avoid formal/arbitrary constraints (given by present, or mentallities, etc) ?

I would say that is a very fine line to tread. On the one side you hinder what people wish to do, on the other you allow them to make mistakes that did not need to be made. And no two people will agree exactly where that line should be.

[tubar]

I want to complete that if insert errors final term of a multiple equal equation, then will be easily identified where is that error. So additionally is a praise that there are intermediary stages of equals cause i identify easily the error. If the error is in a intermediary equal that is skipped, verry well, error remain there, it doesn't affect my results.

If somebody that read the sheet will see that error very well, will be more cautious about next equations.

But in actual system, if i insert a error in a equation with single equal, then is not error? And if i got that in the sheet is error, I have to search for it and not easy to identify.

But errors can be in text and anywhere.... What if can be errors in a intermediary stage of a equation, if it will be anyway skipped.

[RichardJ]

But in actual system, if i insert a error in a equation with single equal, then is not error? And if i got that in the sheet is error, I have to search for it and not easy to identify.

The problem I have with your proposal is not just that there is potentially an error, but that it is written in a way that would lead others to think that Mathcad did the calculations, and they are therefore much more reliable than they actually are.

[tubar]

all that from mathematics can be exposed in a notebook, Mathcad have to be able too. So to be more flexible when interact with human.

All Mathcad releases was done in aim to be closed to human thinking. So also my proposal go in the way to request a more flexibility from the Mathcad code in a specific problem that does not contradict with mathematics and also not with Mathcad code.

My proposal is a generalisation of the approaches that Mathcad need to do

[tubar]

other example:

t:=a+b

y:=t^2+1

result by "expand option" that y:=a^2+b^2+2*a*b+1

Then why i need mathcad processor to do that, and to consume processing resources of computer, in order to get that final form z:=a^2+b^2+2*a*b+1, and to define a intermediary variable y. I have already the result in mind. And I want to be able to write directly in Mathcad:

y:=t^2+1:=a^2+b^2+2*a*b+1

Why cannot be possible for this simple case ? Indeed for complicated cases I need to use classical path by using common "expand"

[RichardJ]

But you can do that. What is wrong with the way shown in the worksheet? It does exactly what you are asking for, except that it doesn't allow you to type in something for the intermediate expression that is completely wrong.

Edit: I just deleted the previous file, which was saved in Mathcad 11 format. I forgot that it doesn't allow one to hide the keywords and change the appearence of the operators for one expression. The new file is in version 14 format.

[jeanGiraud]

When it comes to manipulate a mathematical form vs another, no CAS will do all. You can check that with Mathematica that has lot more "expansion" than Mathcad/Maple and most likely Mathcad/MuPad. How many equivalent forms, i.e: identities in u words can you find for sin(x) = several [we exclude the series and the like series]. For sin(1.23456789) Mathcad gets it from the Pentium, it's fast but still infinitely slow when it comes to Fourier fft's. That is just to show how useless a representation may be. Again, my point here is about that an equality is uniquely used for solving.

Here, if you think both expressions are equal,

they are not because they are both wrong.

Visit "Mathcad usage", Integral ill posed Integrand

jmG