Advertising they push the idea that in a spreadsheet a formula always look like:
Ok! may prefer it to look something like the following, but for such a simple expression I'm not going to pay the price of MathCAD for such limited additional benefit.
Google subtracts MathML from Chrome, and anger multiplies
Therefore first presentation of the formula is by image, the formula above was copy pasted using the MS Equation object in MS Excel and copy pasted into MS paint. So the more complex formula presented as an image is:
This image was obtained from a screen capture from Amaya, where I created the equation using its equation editor for MathML as can be seen in the following:
Any case if MathML works in your browser (firefox, Amaya should work) then the following should render similar to the image. If MathML not working then ignore, the equation is not valid.
So that is the equation, and arguably the vertical style presentation is more readable than the single line presentation. When reading text books and industry manuals its definitely more familiar and recognisable, that doesn't however make it any easier to understand.
One thing I skipped in my little exercise was to actually time each application used. Any case since I am more familiar with Excel than any of the other applications, timing wouldn't really be fair any case. So the following are use of SMath Studio , its similar to MathCAD, I also used FreeMat which is similar to MatLAB , there are other free software variations of MatLAB: these are Octave and SciLAB. here is an interesting article on MatLAB alternatives.
Speed wise in terms of getting the number I wanted, the order was MS Excel, FreeMat, then SMath.
Here is the screen capture of the MS Excel version, which does highlight one problem, the equation presented above the result doesn't relate to the actual formula in the cell. That is largely because I copied the formula from my vba code to set up the calculation, not from the result cell.
Correcting for this here is a better view, this time with the cursor highlighting the edit bar for the calculated work cell, so that the calculated formula can be seen.
Has can be seen the formula is not based on cell references but on named ranges. Though it could be presented in the following manner. This time the formula is based on cell references, but an equation object has been presented above the result. However it is only an image of the formula, and if change the formula then it doesn't update. A better option would be too make use of XLC.
The following is the screen capture for SMath Studio, unlike Amaya, the equation editor worked by my typing in the single line format of the expression. As you type it reformats the expression. Copying and pasting an expression from elsewhere doesn't seem to work well, and editing had some problems. All up it gave me the wrong answer in the first instance. At first I thought there may have been conflict between Young's modulus E and the base of natural logarithms e, so I replace E with Y. But that didn't help, I also made some of the variables single character (I couldn't figure out how to subscript variable names, I could only find options for matrices, and I figure that would produce a different type of variable), and I removed underscores from the names. None of it helped. So I deleted the expression and started again from scratch, and that worked. I then started editing and changing the variable names back. So first lesson, just because the expression is nicely formatted, doesn't mean that it bears any relationship to the behind the scenes translation into a calculated result. The answer I got in the first instance was 9 point something: way out.
Since I got an error, I decided to track down what part of the calculation was potentially at fault. So I extended the Excel spreadsheet and the SMath calculation page, rewriting the expression as Eq1+(1+Eq2) as follows:
Whether we use Excel or MathCAD or even Mathematica , it important to understand that a great deal of translation is going on behind the scenes. To start with, we may prefer the use of infix notation for our mathematical expressions, computers on the other hand prefer post fix (or reverse Polish notation RPN), so arithmetic expressions we type in have to be parsed and translated into a stack of numbers and operators to be fed to the computers arithmetic processing unit. How the expression is displayed and how it is represented behind the scenes for calculation purposes are two different things. Similarly how the expression is input can be yet another data structure and processing task.
Our regulations require independent technical check. I would contend that independence is not achieved if designer and certifier are using the same software. Therefore both should not use MathCAD. Further just because have expression displayed, and results supposedly calculated from that expression doesn't mean that it is all valid. I contend that an independent technical check does not take place if the certifier has the designers calculations, and is reading those calculations. The certifier should have a blank sheet, for a valid independent check.
So having identified that one part of my expression was messed up by attempting to copy/paste equation segments. I decided to have a try with FreeMAT to see how cumbersome that would be, the following is the screen capture from.
|Calculation in FreeMat|
But from another viewpoint, I spend as much time in the vba editor behind Excel as I do using Excel worksheets. So the FreeMat type environment does have its attraction, the issue for me is I have a lot of vba code, and translating to yet another application language is wasteful of my time.
There are also a multitude of simpler computer based calculators with tracing of the calculations, or specialised versions of interpreted Basic programming environment for engineering. For example to name a few:
- ATCalc, version 4.0 (This now taken over from my use of Calc98 using RPN via my computer keyboard or the mouse was/is a pain: it also doesn't trace (But it does have a lot of other useful features). Just typing expression into ATCalc is easier and get a trace if have results panel switched on.)
- Microsoft Mathematics
- Math Mechanixs
|ATCalc with results panel switched off, simple and unobtrusive|
Checking using firefox, the MathML in the blog post displays correctly, though possibly too small.