Check this carefully

spn=1000; w=1.093; tareacable=0.005044; initialslack=0.01; strainlimub=0.5;
strainincrement=0.1; slack=initialslack;
iters=(spn*strainlimub-200*initialslack)/(100*strainincrement)+1;
i=1;slacdataStrain=Table[0,{i,1,iters}]; slacdataTension=Table[0,{i,1,iters}];
While[(slack/spn)*100<strainlimub,
  slacdataStrain[[i]]= slack/spn*100; 
  slacdataTension[[i]]=H/.FindRoot[{((2*(H/w)*Sinh[spn*w/(2*H)]-spn-slack)/tareacable)},{H,1000}]; 
  slack=slack+strainincrement; 
  i++];
points=Transpose[{slacdataStrain,slacdataTension}];
ListPlot[points]

There are a number of warning messages printed which may indicate that no sufficiently precise roots were able to be found for some values of your parameters.

Perhaps most of the way I arrange code when posting here is not so important. I try to provide complete working examples so that anyone can scrape it off the screen and paste it into Mathematica and it should run.I often squeeze the more ordinary parts of the initialization code into a few lines to try to take the minimal amount of space on the screen . That is an attempt to leave more room for and to highlight the more essential parts of the code. Looking for any subtle specific differences between my code and your code, ignoring the formatting, is probably much more important. And, as I mentioned, just reformatting the code may be a very low priority when compared to your need to get the code working. My latest post wasn't intended to show you how to format your code. The only intent was to show how you might avoid creating multiple lists to hold results and then filling those lists with coefficients and then reformatting those results for your final purpose.

Using the Mathematica Function[] had some implications and differences from the generic concept of "function" in mathematics. I cannot be certain, but from your four sentence description of what you are seeing, I am assuming that Mathematica is giving some subtle feedback that it thinks there may a problem with the code you have given it. I have no idea what your real purpose is or your expected use is of these polynomial definitions. Given that I think the most I can do is to suggest carefully reading the help pages for Function and in particular clicking on the orange "Details" and try to determine whether it seems like there might possibly be implications from using Function that may not be exactly compatible with what you are trying to do. If that isn't sufficient then perhaps posting the code for a simple example of a couple of your polynomials followed by the code and explanation of what you want to then do with these polynomials might help. Perhaps that would let someone understand what you need to know.

I like the way you've arranged it, from past practice I've been coding one item per row but this is more organized. Perhaps IF I get what i want working, I'll come back and tidy up.

Why does MM complain about simple polynomial functions such as these? I have about a dozen 4th order polynomials to define, and they all are a function of x. x=.3 outlayer=Function[a0+a1* x+a2* x^2+a3* x^3+a4* x^4] inlayer=Function[b0+b1* x+b2* x^2+b3* x^3+b4* x^4]

One of the definitions is shadowed, in this case x is. Can this be ignored?

Thanks much. I had reviewed use of /. prior to posting but did not make the connection the variable name is referred to rather than just the output.(which almost works btw)

G

Thanks for taking the time to review. I've updated the attached file to show exactly what I've mentioned in my first post. The second file is a screenshot from Prime 3.1 with the same process and variables. The two outputs agree and the output is as expected, so I don't think at any of the increments the program fails to converge but that said I'm not that familiar yet with Mathematica's warnings on precision. The plot, and eventually to be a manipulated plot I wish to prepare shows a transmission line stranded cable horizontal tension H as a function of strain in a suspended catenary. G

Attachments:

Capture.JPG

HyperAAGP.nb