Thanks Ibrahim,
I have used the context help, and it is good as far as it goes. But in regard to the completeness of the documentation, there is a reason for that.
There is another system we all know about it that is incredibly widely used. It is called the Decimal System. The Decimal System is easily documented. So easy, in fact, many people who use it could document it completely in a few minutes. Now think about another system that is impossible to completely document. It is called the Roman Numeral System. In the Roman Numeral System, in order to make bigger numbers, it is necessary to invent new conventions of representation.
One system is completely systematic with a necessary and sufficient set of rules, and the other is ad hoc and open ended and requires new conventions in order to create larger and larger numbers. Please note how much more one of these systems is used than the other. Tthat alone tells me that just how worthy it is to strive to make our systems more like the Decimal System and less like the Roman Numeral System.
Mathcad is not bad as systems go, in regard to ease of use and the like...but like most systems it is, in fact, very mediocre compared to the real limits of just how good it really could be.
Here is a short sampling of how Mathcad is "Roman Numeral" like. I don't think the Mathcad syntax and behavior was thought out very carefully in regard to a number of concerns. So Mathcad is maybe a bit better than typical, but in no way any where near what it could be. Remember world markets run in the billions.
Here are examples of just one small area of syntax/behavior of how Mathcad is more "Roman Numeral" like than "Decimal" like. Mathcad is more or less impossible to completely document. The very best syntax and set of conventions would not have these kinds of problems.
I'm sorry I'm such a grouch about Mathcad...but there is Prime coming down the line, and I hope....or at least wish...that they would make it better in these regards. I haven't actually seen it yet.
John Sellers wrote:
I'm sorry I'm such a grouch about Mathcad...but there is Prime coming down the line, and I hope....or at least wish...that they would make it better in these regards. I haven't actually seen it yet.
Well, lots of luck with that...
Your issues with Mathcad seem somewhat unwarranted, as the issues you've raised are not necessarily issues with Mathcad, per se, but with MATH and its notational limitations. The bottom line is that the multiplication symbol in general usage is overloaded as are many other math symbols and operators. You can check any set of college level math texts and see that. Now, Mathsoft made certain choices in implementing the notation, some good, and some bad. When two vectors are operated upon with a multiplication operator, it makes some sense to interpret that as a dot product. However, squaring a vector is not the equivalent of the dot product of a vector with itself, so some ambiguity exists, which is somewhat outside of the purview of Mathcad.
The very best syntax and set of conventions would not have these kinds of problems.
I disagree that these are problems, and they are well documented.
The documentation for the multiplication operator says:
If x and y are scalars, returns the product of x and y.
If x and y are vectors, returns the dot product (inner product) of x and y, a scalar formed by multiplying element-wise the entries of the first vector with the complex conjugate of the entries of the second vector, and summing the results.
If x and y are matrices, returns the matrix product of x and y.
If one operand is a scalar and the other is a matrix, each element in the matrix is multiplied by the scalar.
So the default behavior for two vectors is the dot product. As Eden points out, that is not the same as squaring a vector because there is no accepted definition of what that means. So, like many other operators and functions in Mathcad, when you square a vector what you get is the operator applied element by element. This is documented. The description of the exponentiation operator says:
If y is a scalar and x is a vector, the result is a vector of the same size as x, whose ith entry is y raised to the power xi.
As far as nested matrices go, the behavior is also documented:
Most of Mathcad's operators and functions do not work with nested arrays, since there is no universally accepted definition of what constitutes correct behavior in this context. Certain operators and functions are nevertheless useful and appropriate for nested arrays. Functions that enumerate rows or columns and functions that partition, augment, and stack matrices, can be applied to nested arrays. The transpose, subscript, and column array operators and the Boolean equal sign all support nested arrays.
Mostly documented, anyway. It doesn't actually say that multiplication by a scalar is permitted, even though it obviously is.
