Expression of type ExprTuple

from the theory of proveit.linear_algebra.tensors

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, gamma, i, x, y
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import InSet
from proveit.numbers import Add, Interval, four, one, two

# build up the expression from sub-expressions
sub_expr1 = InSet(i, Interval(two, four))
sub_expr2 = ScalarMult(beta, ScalarMult(Add(i, one), TensorProd(x, y)))
expr = ExprTuple(Lambda(i, Conditional(ScalarMult(gamma, ScalarMult(i, sub_expr2)), sub_expr1)), Lambda(i, Conditional(ScalarMult(ScalarMult(gamma, i), sub_expr2), sub_expr1)))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(i \mapsto \left\{\gamma \cdot \left(i \cdot \left(\beta \cdot \left(\left(i + 1\right) \cdot \left(x {\otimes} y\right)\right)\right)\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right.., i \mapsto \left\{\left(\gamma \cdot i\right) \cdot \left(\beta \cdot \left(\left(i + 1\right) \cdot \left(x {\otimes} y\right)\right)\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right..\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Lambda	parameter: 35 body: 3
2	Lambda	parameter: 35 body: 5
3	Conditional	value: 6 condition: 8
4	ExprTuple	35
5	Conditional	value: 7 condition: 8
6	Operation	operator: 27 operands: 9
7	Operation	operator: 27 operands: 10
8	Operation	operator: 11 operands: 12
9	ExprTuple	21, 13
10	ExprTuple	14, 20
11	Literal
12	ExprTuple	35, 15
13	Operation	operator: 27 operands: 16
14	Operation	operator: 27 operands: 17
15	Operation	operator: 18 operands: 19
16	ExprTuple	35, 20
17	ExprTuple	21, 35
18	Literal
19	ExprTuple	22, 23
20	Operation	operator: 27 operands: 24
21	Variable
22	Literal
23	Literal
24	ExprTuple	25, 26
25	Variable
26	Operation	operator: 27 operands: 28
27	Literal
28	ExprTuple	29, 30
29	Operation	operator: 31 operands: 32
30	Operation	operator: 33 operands: 34
31	Literal
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	37, 38
35	Variable
36	Literal
37	Variable
38	Variable