I'm building a learning tool where students are required to solve/enter mathematical equations. I'm using maxima to compare the answer of the student with the solution entered by the teacher to determine whether or not the student has solved it correctly. I would like to allow equivalent answers but only if they are in their simplest form. So if the answer is a+(b+1)/2, then a+(1+b)/2, (b+1)/2+a and (1+b)/2+a are also correct, but a+(2b+2)/4 is not.
Is there a way to do this in maxima?
I tried using ratsimp to simplify the expression and then check if it has remained the same, if so it would mean it was already in its simplest form. Unfortunately, if I use this on a+b for instance, it changes the order of the variables to b+a. Is there some way to check if two expressions are identical except for the order of the operations?
For future reference, I found that you can use the following:
args(expression), simp: false
This will return an array of all the arguments, without simplifying, which we then can use to check if this array is the same for two expressions except for the order.
Related
https://en.wikibooks.org/wiki/Lua_Programming/Statements says:
Statements are pieces of code that can be executed and that contain an
instruction and expressions to use with it. Some statements will also
contain code inside of themselves that may, for example, be run under
certain conditions. Dissimilarly to expressions, they can be put
directly in code and will execute.
What does it mean by instructions?
Am I looking too deep in to it
That article seems very poorly written in general. Containing gems like "Assignment is [...] used to assign". Your confusion is probably also just a result of this awkward style. The way I read it, the book separates between:
Statements: Do something specific, like adding two values into a variable.
Instructions: Things you can do in general, like adding any two values.
It seems to suggest a sort of abstraction-application relationship between the two.
That's a very specific way of dividing between the two and it's ultimately very inconsequential, so you can probably treat them as interchangeable while reading that book.
I should check existence of values based on some conditions.
i.e. i have 3 variables, varA, varB and varC. varC should not be empty only if varA>varB (condition).
i normally use some syntax to check any of the variables and run a frequency of any of them to see if there are errors:
if missing(varC) and (varA>varB) ck_varC=1.
if not(missing(varC)) and not(varA>varB) ck_varC=2.
exe.
fre ck_varC.
exe.
I had some errors when the condition became complex and when in the condition there are missing() or other functions but i could have made a mistake.
do you think there is an easier way of doing this checks?
thanks in advance
EDIT: here an example of what i mean, think at a questionnaire with some routing, you ask age to anyone, if they are between 17 and 44 ask them if they work, if they work ask them how many hours.
i have an excel tool where i put down all variables with all conditions, then it will generate the syntax in the example, all with the same structure for all variables, considering both situations, we have a value that shouldn't be there or we don't have a value that should be there.
is there an easier way of doing that? is this structure always valid no matter what is the condition?
In SPSS, missing values are not numbers. You need to explicitly program those scenarios as well. you got varC covered (partially), but no scenario where varA or varB have missing data is covered.
(As good practice, maybe you should initialize your check variable as sysmis or 0, using syntax):
numeric ck_varC (f1.0).
compute ck_varC=0.
if missing(varC) and (varA>varB) ck_varC=1.
if not(missing(varC)) and not(varA>varB) ck_varC=2.
***additional conditional scenarios go here:.
if missing(varA) or missing(varB) ck_varC=3.
...
fre ck_varC.
By the way - you do not need any of the exe. commands if you are going to run your syntax as a whole.
Later Edit, after the poster updated the question:
Your syntax would be something like this. Note the use of the range function, which is not mandatory, but might be useful for you in the future.
I am also assuming that work is a string variable, so its values need to be referenced using quotation signs.
if missing(age) ck_age=1.
if missing(work) and range(age,17,44) ck_work=1.
if missing(hours) and work="yes" ck_hours=1.
if not (missing (age)) and not(1>0) ck_age=2. /*this will never happen because of the not(1>0).
if not(missing(work)) and (not range(age,17,44)) ck_work=2. /*note that if age is missing, this ck_work won't be set here.
if not(missing(hours)) and (not(work="yes")) ck_hours=2.
EXECUTE.
String variables are case sensitive
There is no missing equivalent in strings; an empty blank string ("") is still a string. not(work="yes") is True when work is blank ("").
I'm using Z3 with the ml interface. I had created a formula
f(x_i)
that is satisfiable, according to the solver
Solver.mk_simple_solver ctxr.
The problem is: I can get a model, but he find me values only for some variables of the formula, and not all (some of my Model.get_const_interp_er end with a type None)
How can it be possible that the model can give me only a part of the x_ir? In my understanding, if the model work for one of the values, it means that the formula was satisfiable (in my case, it is) and so all the values can be given...
I don't understand something..
Thanks for reading me!
You should always post full examples so people can help with actual coding issues; without seeing your actual code, it's impossible to know what might be the actual reason.
Having said that, this sounds very much like the following question: Why Z3Py does not provide all possible solutions So, perhaps the answer given there will help you.
Long story short: Z3 models will only contain values for variables that matter for the model. For anything that is not explicitly assigned, any value will do. There are ways to get "full" models as explained in that answer of course; which I'm sure is also possible from the ML interface.
I currently have the following pattern embedded inside a larger computation
seq1.isin(seq2[seq3].unique().compute().values)
where seq3 is a boolean Series.
The performance seems acceptable, but it is ugly and the use of compute() forces evaluation, possibly removing opportunities for parallelism.
Simply saying
seq1.isin(seq2[seq3].unique())
does not work and the documentation says that the argument to isin must be an (I presume Numpy) array.
Is there a bettern way to write the above code?
What if seq1 and seq2 are the same?
I don't think it's possible do an incremental set membership operation. To get a correct result, you'd need to have a fully realized set to answer the question of whether an item is a member of it or not.
You could probably achieve this operation using an inner join.
I have asked a few questions about this recently and I am getting where I need to go, but have perhaps not been specific enough in my last questions to get all the way there. So, I am trying to put together a structure for calculating some metrics based on app data, which should be flexible to allow additional metrics to be added easily (and securely), and also relatively simple to use in my views.
The overall goal is that I will be able to have a custom helper that allows something like the following in my view:
calculate_metric(#metrics.where(:name => 'profit'),#customer,#start_date,#end_date)
This should be fairly self explanatory - the name can be substituted to any of the available metric names, and the calculation can be performed for any customer or group of customers, for any given time period.
Where the complexity arises is in how to store the formula for calculating the metric - I have shown below the current structure that I have put together for doing this:
You will note that the key models are metric, operation, operation_type and operand. This kind of structure works ok when the formula is very simple, like profit - one would only have two operands, #customer.sales.selling_price.sum and #customer.sales.cost_price.sum, with one operation of type subtraction. Since we don't need to store any intermediate values, register_target will be 1, as will return_register.
I don't think I need to write out a full example to show where it becomes more complicated, but suffice to say if I wanted to calculate the percentage of customers with email addresses for customers who opened accounts between two dates (but did not necessarily buy), this would become much more complex since the helper function would need to know how to handle the date variations.
As such, it seems like this structure is overly complicated, and would be hard to use for anything other than a simple formula - can anyone suggest a better way of approaching this problem?
EDIT: On the basis of the answer from Railsdog, I have made some slight changes to my model, and re-uploaded the diagram for clarity. Essentially, I have ensured that the reporting_category model can be used to hide intermediate operands from users, and that operands that may be used in user calculations can be presented in a categorised format. All I need now is for someone to assist me in modifying my structure to allow an operation to use either an actual operand or the result of a previous operation in a rails-esqe way.
Thanks for all of your help so far!
Oy vey. It's been years (like 15) since I did something similar to what it seems like you are attempting. My app was used to model particulate deposition rates for industrial incinerators.
In the end, all the computations boiled down to two operands and an operator (order of operations, parentheticals, etc). Operands were either constants, db values, or the result of another computation (a pointer to another computation). Any Operand (through model methods) could evaluate itself, whether that value was intrinsic, or required a child computation to evaluate itself first.
The interface wasn't particularly elegant (that's the real challenge I think), but the users were scientists, and they understood the computation decomposition.
Thinking about your issue, I'd have any individual Metric able to return it's value, and create the necessary methods to arrive at that answer. After all, a single metric just needs to know how to combine it's two operands using the indicated operator. If an operand is itself a metric, you just ask it what it's value is.