# from the theory of proveit.physics.quantum.QPE¶

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.
# import Expression classes needed to build the expression
from proveit import ExprTuple, e
from proveit.numbers import Add, Less, LessEq, Neg, one
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

In [2]:
# build up the expression from sub-expressions
sub_expr2 = Neg(sub_expr1)
expr = ExprTuple(LessEq(Add(Neg(_two_pow__t_minus_one), one), sub_expr2), Less(sub_expr2, sub_expr1), LessEq(sub_expr1, _two_pow__t_minus_one))

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(\left(-2^{t - 1} + 1\right) \leq \left(-\left(e + 1\right)\right), \left(-\left(e + 1\right)\right) < \left(e + 1\right), \left(e + 1\right) \leq 2^{t - 1}\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1, 2, 3
1Operationoperator: 7
operands: 4
2Operationoperator: 5
operands: 6
3Operationoperator: 7
operands: 8
4ExprTuple9, 10
5Literal
6ExprTuple10, 14
7Literal
8ExprTuple14, 17
9Operationoperator: 23
operands: 11
10Operationoperator: 27
operand: 14
11ExprTuple13, 29
12ExprTuple14
13Operationoperator: 27
operand: 17
14Operationoperator: 23
operands: 16
15ExprTuple17
16ExprTuple18, 29
17Operationoperator: 19
operands: 20
18Variable
19Literal
20ExprTuple21, 22
21Literal
22Operationoperator: 23
operands: 24
23Literal
24ExprTuple25, 26
25Literal
26Operationoperator: 27
operand: 29
27Literal
28ExprTuple29
29Literal