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Expression of type LessEq

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import eps, n, t
from proveit.numbers import Add, Ceil, Log, Mult, frac, greater_eq, one, two
In [2]:
# build up the expression from sub-expressions
expr = greater_eq(t, Add(n, Ceil(Log(two, Add(two, frac(one, Mult(two, eps)))))))
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())
t \geq \left(n + \left\lceil \textrm{log}_2\left(2 + \frac{1}{2 \cdot \epsilon}\right)\right\rceil\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalreversed('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 14
operands: 5
4Variable
5ExprTuple6, 7
6Variable
7Operationoperator: 8
operand: 10
8Literal
9ExprTuple10
10Operationoperator: 11
operands: 12
11Literal
12ExprTuple23, 13
13Operationoperator: 14
operands: 15
14Literal
15ExprTuple23, 16
16Operationoperator: 17
operands: 18
17Literal
18ExprTuple19, 20
19Literal
20Operationoperator: 21
operands: 22
21Literal
22ExprTuple23, 24
23Literal
24Variable