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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, fi, i, x, z
from proveit.linear_algebra import TensorProd
from proveit.logic import CartExp, InSet
from proveit.numbers import Interval, Real, one, three
In [2]:
# build up the expression from sub-expressions
sub_expr1 = CartExp(Real, three)
expr = Lambda(i, Conditional(InSet(TensorProd(x, fi, z), TensorProd(sub_expr1, sub_expr1, sub_expr1)), InSet(i, Interval(one, three))))
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(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 \{1~\ldotp \ldotp~3\}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 24
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 5
operands: 4
3Operationoperator: 5
operands: 6
4ExprTuple7, 8
5Literal
6ExprTuple24, 9
7Operationoperator: 11
operands: 10
8Operationoperator: 11
operands: 12
9Operationoperator: 13
operands: 14
10ExprTuple15, 16, 17
11Literal
12ExprTuple18, 18, 18
13Literal
14ExprTuple19, 26
15Variable
16Operationoperator: 20
operand: 24
17Variable
18Operationoperator: 22
operands: 23
19Literal
20Variable
21ExprTuple24
22Literal
23ExprTuple25, 26
24Variable
25Literal
26Literal