Mathcad 15 Guide

[Paz Warsager]

Nextopen the Windows Calculator program again, and put it in "programmer mode". Press "HEX", then enter "7FFF FFFF FFFF FFFF" (don't type in the blanks, which I have inserted to help you count the number of "F's). This is the largest positive integer that can be represented with 64 bits . What does the "DEC" line show?

Any decimal number whose least significant digit is 6, when raised to any positive integer power, gives a result that also has 6 as its least significant digit. The result on left of the claimed equality (after adding +1 to both sides), however, ends with 8, as stated earlier. The equality claim is refuted.

thanks for this info. i will study it. what your saying is weird though, because i did the calculations in Mathcad (about a month or two ago) and it shows what I posted. so i'm not sure what is going on. also, the microsoft help shows the difference for signed and unsigned and it's not a big difference. the difference from the intel manual is 50%.

In these discussions, one needs to keep in mind that finite-precision computer arithmetic does not always obey the rules of mathematics. As a consequence, when arguments are stated, one has to make it clear whether some associated calculations were made using classical mathematics or computer arithmetic.

unfortunately, it's not very clear to me. i attached a document with calculations i did awhile ago. in an attempt to figure out what was going on. it seems to be a dead end. however, it did make me realize there seems to be an error in the intel manual. unless of course, i'm just hopelessly lost.

the document looks at various definitions I found of the supposed limit. none of which even come close to the limit I'm experiencing. however, that topic is in a different thread. i made this thread just to point out an issue with the intel user manual.

maybe i confused you. i added brackets to my original post. the number you showed in your link wasn't the number i meant. i can see where my original post wasn't clear. i literally copied that from the intel manual though. in any event, maybe the updated post explains what i mean better.

The beauty of using LISP is you learn that the brackets are really important. Fortran tends to get sloppy and not use them and rely on the standard rules of math conventions. You half used brackets which is dangerous in long Fortran equations.

Do you think that there is something wrong with this entry in the table? Do you recognize that this is the upper limit on the loop count, and that DO loop index variables can start with a large negative number as the starting value, as I illustrated with the short program in my earlier reply?

The exact nature of the computations that are performed for a DO loop with a loop-control triplet of integers is specified by the standard. There is a further "guard-rail" that the program source is invalid if during the course of those calculations an integer overflow occurs.

i think there is a lot of confusion. i didn't program this in fortran. i was just trying to understand what the limit is. i used Mathcad. In Mathcad, there is no problem calculating 2^(63-1). the pdf file that I attached is a copy of the Mathcad file. it also has the references etc. plus a bunch of comparisons. i still think the intel manual doesn't make sense. their statement that:

really weird. i put what you said into mathcad and it gives the right answer. so the intel manual is 2^63-1. mathcad gives 2^63 as the same number. whether i subtract one or not. the confusion started from other documents online. i get what you are saying though. thanks for clarifying

Searching the web turned up this link about Mathcad from the year 2008, which discusses something quite similar with integers near the limit of what can be represented in 32 bits. Specifically, the complaint was that the version of Mathcad in use at that time gave a negative value for 231. We seem to be experiencing a redux of the same problem near the limit of 64 bits, fifteen years later.

the version i have of mathcad is old and hasn't changed much. mathcad prime is the new stuff. however, from what i've read, and the licensing, i'm not interested in it. however, i don't think this was mathcad's fault. i just got confused from the get go and happened to be getting numbers that looked right (that aspect may be mathcad's fault though). i am updating the files with the correct formula (that you explained).

as for what i've been seeing in testing. i think there might be several things going on. i basically can run 1.0d5 on any code and it's fast. i've been using that for decades. i have 16gb of memory and that seems to be pretty close to 1.0d5 (maybe just a coincidence, but I'm starting to wonder if that's significant). depending on the code, the limit i'm hitting is 1.0d6, 1.0d7, or 2.0d8. I think the last one might be with allocatable arrays. not 100% sure, at the moment. in any event, they are all below the 32gb limit. i tried increasing the page file but it didn't seem to do anything. i'm wondering if i actually had 64gb of memory, maybe all this would be a lot different. as it stands, 1.0d5 runs as expected. if i do nothing but switch to allocatable arrays it slows down. so the gflops are lower than they should be. that's all i know at the moment. i'll post more on the other thread, if i find out anything useful.

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PTC Mathcad Prime offers a robust platform for solving equations symbolically, a capability that is indispensable for engineers and scientists. By leveraging the symbolic computation power of Mathcad Prime, users can perform complex mathematical manipulations and arrive at analytical solutions for equations and expressions. In this step-by-step guide, we will illustrate how to navigate through the process of symbolic solving, including the utilization of the symbolic "solve" keyword and techniques for extracting solutions.

The "solve" keyword in PTC Mathcad Prime is a fundamental tool for symbolic calculations. To solve an equation symbolically, navigate to the Symbolics list in the Operations and Symbols group under the Math tab. With a simple click, Mathcad Prime attempts to solve the equation and generally returns the solutions in a vector format, as real numbers, or as complex numbers when applicable.

Symbolic solutions obtained in Mathcad Prime can be assigned to a variable for easy reference in subsequent calculations. If the solution set is returned as a vector, one can extract individual solutions from this vector. For example, once you assign the solution vector to a variable "S", you can extract the first solution with "S[0]" and the second solution with "S[1]", where the square brackets indicate the index of the solution in the vector.

It is often necessary to convert symbolic solutions into numeric approximations. Mathcad Prime allows users to perform this operation seamlessly. By selecting the symbolic solution and using the "float" option from the Symbolics toolbar, users can obtain numeric representations of their solutions to the desired degree of precision.

Mathcad Prime also excels in handling systems of equations. When presented with simultaneous equations, the user must first arrange these equations into a matrix or vector form. After indicating the unknowns to be solved for, Mathcad Prime can symbolically solve these equations, providing solutions in a structured format that allows for easy interpretation and extraction.

First Example: Consider a simple quadratic equation. After entering the equation, place the cursor behind it, select the solve option from the Symbolics toolbar, and click outside the region to execute the operation. You will be presented with symbolic solutions, which can then be assigned to a variable and extracted as described earlier.

Second Example: When dealing with a system of equations with multiple unknowns, such as "x", "y", "a", and "b", it is vital to specify which variables to solve for. After doing so, Mathcad Prime will return the solutions for the specified variables. These solutions may be arranged in a row vector, and you can use matrix indexing to extract individual solutions, such as "[0,0]" for the first solution.

This guide provides a blueprint for utilizing PTC Mathcad Prime's symbolic solving capabilities. Mastery of these techniques opens the door to advanced analytical problem-solving, allowing users to tackle a wide array of mathematical challenges within the engineering and scientific domains. Whether you are solving single equations or complex systems, Mathcad Prime facilitates an intuitive and powerful environment for symbolic computation.

For those looking to extend their toolkit further, NOVEDGE offers a range of compatible and complementary software solutions. For instance, users can integrate MathCAD with PTC Creo for powerful engineering calculations alongside 3D CAD design. Additionally, for advanced rendering and animation, solutions like V-Ray or MAXON's Cinema 4D can be employed to bring visualizations to the next level.

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