Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

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, k
from proveit.linear_algebra import ScalarMult
from proveit.logic import InSet
from proveit.numbers import Add, Exp, Interval, Mult, e, i, one, pi, two, zero
from proveit.physics.quantum import Ket
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
sub_expr1 = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), Ket(k))
expr = ExprTuple(Conditional(sub_expr1, InSet(k, Interval(Add(zero, one), one))), Conditional(sub_expr1, InSet(k, Interval(one, one))))

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(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle \textrm{ if } k \in \{0 + 1~\ldotp \ldotp~1\}, \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle \textrm{ if } k \in \{1~\ldotp \ldotp~1\}\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	Conditional	value: 4 condition: 3
2	Conditional	value: 4 condition: 5
3	Operation	operator: 9 operands: 6
4	Operation	operator: 7 operands: 8
5	Operation	operator: 9 operands: 10
6	ExprTuple	35, 11
7	Literal
8	ExprTuple	12, 13
9	Literal
10	ExprTuple	35, 14
11	Operation	operator: 20 operands: 15
12	Operation	operator: 16 operands: 17
13	Operation	operator: 18 operand: 35
14	Operation	operator: 20 operands: 21
15	ExprTuple	22, 30
16	Literal
17	ExprTuple	23, 24
18	Literal
19	ExprTuple	35
20	Literal
21	ExprTuple	30, 30
22	Operation	operator: 25 operands: 26
23	Literal
24	Operation	operator: 27 operands: 28
25	Literal
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	31, 32, 33, 34, 35
29	Literal
30	Literal
31	Literal
32	Literal
33	Literal
34	Literal
35	Variable