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Expression of type ExprTuple

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, ExprTuple, Lambda, beta, fi, gamma, i
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, InSet
from proveit.numbers import Interval, Mult, four, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = InSet(i, Interval(two, four))
expr = ExprTuple(Lambda(i, Equals(Conditional(ScalarMult(ScalarMult(gamma, beta), fi), sub_expr1), Conditional(ScalarMult(Mult(gamma, beta), fi), sub_expr1))))
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(i \mapsto \left(\left\{\left(\gamma \cdot \beta\right) \cdot f\left(i\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right.. = \left\{\left(\gamma \cdot \beta\right) \cdot f\left(i\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right..\right)\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameter: 27
body: 2
2Operationoperator: 3
operands: 4
3Literal
4ExprTuple5, 6
5Conditionalvalue: 7
condition: 9
6Conditionalvalue: 8
condition: 9
7Operationoperator: 18
operands: 10
8Operationoperator: 18
operands: 11
9Operationoperator: 12
operands: 13
10ExprTuple14, 16
11ExprTuple15, 16
12Literal
13ExprTuple27, 17
14Operationoperator: 18
operands: 20
15Operationoperator: 19
operands: 20
16Operationoperator: 21
operand: 27
17Operationoperator: 23
operands: 24
18Literal
19Literal
20ExprTuple25, 26
21Variable
22ExprTuple27
23Literal
24ExprTuple28, 29
25Variable
26Variable
27Variable
28Literal
29Literal