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Expression of type Lambda

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, Lambda, beta, fi, gamma, i, x, y
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import InSet
from proveit.numbers import Interval, four, two
In [2]:
# build up the expression from sub-expressions
expr = Lambda(i, Conditional(ScalarMult(ScalarMult(gamma, beta), TensorProd(x, fi, y)), 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())
i \mapsto \left\{\left(\gamma \cdot \beta\right) \cdot \left(x {\otimes} f\left(i\right) {\otimes} y\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 25
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 10
operands: 4
3Operationoperator: 5
operands: 6
4ExprTuple7, 8
5Literal
6ExprTuple25, 9
7Operationoperator: 10
operands: 11
8Operationoperator: 12
operands: 13
9Operationoperator: 14
operands: 15
10Literal
11ExprTuple16, 17
12Literal
13ExprTuple18, 19, 20
14Literal
15ExprTuple21, 22
16Variable
17Variable
18Variable
19Operationoperator: 23
operand: 25
20Variable
21Literal
22Literal
23Variable
24ExprTuple25
25Variable