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Expression of type Conditional

from the theory of proveit.linear_algebra.tensors

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, fi, i, x, z
from proveit.linear_algebra import TensorProd
from proveit.logic import CartExp, InSet
from proveit.numbers import Interval, Real, four, three, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = CartExp(Real, three)
expr = Conditional(InSet(TensorProd(x, fi, z), TensorProd(sub_expr1, sub_expr1, sub_expr1)), InSet(i, Interval(two, four)))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left\{\left(x {\otimes} f\left(i\right) {\otimes} z\right) \in \left(\mathbb{R}^{3} {\otimes} \mathbb{R}^{3} {\otimes} \mathbb{R}^{3}\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 4
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 7
4Literal
5ExprTuple24, 8
6Operationoperator: 10
operands: 9
7Operationoperator: 10
operands: 11
8Operationoperator: 12
operands: 13
9ExprTuple14, 15, 16
10Literal
11ExprTuple17, 17, 17
12Literal
13ExprTuple18, 19
14Variable
15Operationoperator: 20
operand: 24
16Variable
17Operationoperator: 22
operands: 23
18Literal
19Literal
20Variable
21ExprTuple24
22Literal
23ExprTuple25, 26
24Variable
25Literal
26Literal